Chapter 3 Review Algebra 1 Answers 3-1 Through 3-3

Chapter 3 Review Exercises

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    18494
  • Chapter Review Exercises

    Graph Linear Equations in Two Variables

    Plot Points in a Rectangular Coordinate Arrangement

    In the post-obit exercises, plot each signal in a rectangular coordinate system.

    1. ⓐ \((−one,−v)\)
    ⓑ \((−3,4)\)
    ⓒ \((2,−3)\)
    ⓓ \((1,\frac{5}{2})\)

    Answer

    This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 5 to 5. The point labeled a is 1 units to the left of the origin and 5 units below the origin and is located in quadrant III. The point labeled b is 3 units to the left of the origin and 4 units above the origin and is located in quadrant II. The point labeled c is 2 units to the right of the origin and 3 units below the origin and is located in quadrant IV. The point labeled d is 1 unit to the right of the origin and 2.5 units above the origin and is located in quadrant I.

    2. ⓐ \((−two,0)\)
    ⓑ \((0,−4)\)
    ⓒ \((0,5)\)
    ⓓ \((3,0)\)

    In the following exercises, decide which ordered pairs are solutions to the given equations.

    3. \(5x+y=x\);

    ⓐ \((5,ane)\)
    ⓑ \((two,0)\)
    ⓒ \((4,−10)\)

    Answer

    ⓑ, ⓒ

    iv. \(y=6x−2\);

    ⓐ \((1,4)\)
    ⓑ \((13,0)\)
    ⓒ \((6,−2)\)

    Graph a Linear Equation by Plotting Points

    In the following exercises, graph by plotting points.

    five. \(y=4x−iii\)

    Answer

    This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 1, negative 7), (0, negative 3), (1, negative 1), and (2, 3).

    6. \(y=−3x\)

    7. \(y=\frac{1}{two}x+3\)

    Answer

    This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 6, 0), (0, 3), (2, 4), and (4, 5).

    8. \(y=−\frac{4}{five}|ten−one\)

    nine. \(10−y=6\)

    Reply

    This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 1, negative 7), (0, negative 6), (3, negative 3), and (6, 0).

    x. \(2x+y=7\)

    11. \(3x−2y=6\)

    Respond

    This figure shows a straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (negative 2, negative 6), (0, negative 3), (2, 0), and (4, 3).

    Graph Vertical and Horizontal lines

    In the following exercises, graph each equation.

    12. \(y=−two\)

    13. \(ten=3\)

    Answer

    This figure shows a vertical straight line graphed on the x y-coordinate plane. The x and y-axes run from negative 8 to 8. The line goes through the points (3, negative 1), (3, 0), and (3, 1).

    In the following exercises, graph each pair of equations in the same rectangular coordinate system.

    14. \(y=−2x\) and \(y=−2\)

    fifteen. \(y=\frac{4}{3}10\) and \(y=\frac{four}{3}\)

    Answer

    The figure shows the graphs of a straight horizontal line and a straight slanted line on the same x y-coordinate plane. The x and y axes run from negative 5 to 5. The horizontal line goes through the points (0, 4 divided by 3), (1, 4 divided by 3), and (2, 4 divided by 3). The slanted line goes through the points (0, 0), (1, 4 divided by 3), and (2, 8 divided by 3).

    Find x- and y-Intercepts

    In the following exercises, observe the 10- and y-intercepts.

    16.
    The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 6, negative 2), (negative 4, 0), (negative 2, 2), (0, 4), (2, 6), and (4, 8).

    17.
    The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 2, 5), (negative 1, 4), (0, 3), (3, 0), and (6, negative 3).

    Answer

    \((0,three)(3,0)\)

    In the following exercises, observe the intercepts of each equation.

    18. \(x−y=−1\)

    nineteen. \(x+2y=half dozen\)

    Answer

    \((6,0),\space (0,three)\)

    20. \(2x+3y=12\)

    21. \(y=\frac{3}{4}x−12\)

    Answer

    \((xvi,0),\space (0,−12)\)

    22. \(y=3x\)

    Graph a Line Using the Intercepts

    In the following exercises, graph using the intercepts.

    23. \(−x+3y=3\)

    Answer

    The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 3, 0), (0, 1), (3, 2), and (6, 3).

    24. \(10−y=4\)

    25. \(2x−y=v\)

    Answer

    The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (0, negative 5), (1, negative 3), (2, negative 1), and (3, 1).

    26. \(2x−4y=8\)

    27. \(y=4x\)

    Answer

    The figure shows a straight line graphed on the x y-coordinate plane. The x and y axes run from negative 8 to 8. The line goes through the points (negative 1, 4), (0, 0), and (1, negative 4).

    Gradient of a Line

    Find the Slope of a Line

    In the following exercises, find the gradient of each line shown.

    28.
    This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (0, 0) and (1, negative 3).

    29.
    This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 4, 0) and (0, 4).

    Answer

    one

    30.
    This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 4, negative 4) and (2, negative 2).

    31.
    This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (1, 4) and (5, 2).

    Answer

    \(−12\)

    In the following exercises, detect the slope of each line.

    32. \(y=2\)

    33. \(x=five\)

    Answer

    undefined

    34. \(x=−3\)

    Use the Slope Formula to find the Slope of a Line between Two Points

    In the following exercises, use the slope formula to find the slope of the line between each pair of points.

    36. \((−1,−i),(0,five)\)

    37. \((three.5),(4,−1)\)

    Answer

    \(−half dozen\)

    38. \((−5,−2),(three,ii)\)

    39. \((2,1),(iv,vi)\)

    Answer

    \(52\)

    Graph a Line Given a Point and the Gradient

    In the following exercises, graph each line with the given signal and slope.

    40. \((2,−2);\space m=52\)

    41. \((−3,iv);\space thousand=−13\)

    Answer

    This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 3, 4) and (0, 3).

    42. \(10\)-intercept \(−4; m=3\)

    43. \(y\)-intercept \(i; m=−34\)

    Answer

    This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (0, 1) and (4, negative 2).

    Graph a Line Using Its Slope and Intercept

    In the following exercises, identify the slope and \(y\)-intercept of each line.

    44. \(y=−4x+9\)

    45. \(y=53x−vi\)

    Answer

    \(m=53;\space (0,−6)\)

    46. \(5x+y=10\)

    47. \(4x−5y=8\)

    Respond

    \(thousand=45;\space (0,−85)\)

    In the following exercises, graph the line of each equation using its slope and y-intercept.

    48. \(y=2x+3\)

    49. \(y=−x−1\)

    Answer

    This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 1) and (1, negative 2).

    50. \(y=−25x+3\)

    51. \(4x−3y=12\)

    Respond

    This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (0, negative 4) and (3, 0).

    In the following exercises, determine the most convenient method to graph each line.

    52. \(x=5\)

    53. \(y=−3\)

    Answer

    horizontal line

    54. \(2x+y=five\)

    55. \(ten−y=2\)

    Answer

    intercepts

    56. \(y=22x+two\)

    57. \(y=34x−i\)

    Reply

    plotting points

    Graph and Interpret Applications of Slope-Intercept

    58. Katherine is a individual chef. The equation \(C=6.5m+42\) models the relation betwixt her weekly cost, C, in dollars and the number of meals, one thousand, that she serves.

    ⓐ Observe Katherine'southward cost for a calendar week when she serves no meals.
    ⓑ Find the cost for a week when she serves xiv meals.
    ⓒ Translate the gradient and C-intercept of the equation.
    ⓓ Graph the equation.

    59. Marjorie teaches pianoforte. The equation \(P=35h−250\) models the relation between her weekly profit, P, in dollars and the number of student lessons, south, that she teaches.

    ⓐ Find Marjorie'due south profit for a week when she teaches no student lessons.
    ⓑ Find the profit for a calendar week when she teaches xx educatee lessons.
    ⓒ Interpret the slope and P-intercept of the equation.
    ⓓ Graph the equation.

    Answer

    ⓐ \(−$250\)
    ⓑ \($450\)
    ⓒ The slope, 35, means that Marjorie's weekly profit, P, increases by $35 for each additional student lesson she teaches.
    The P-intercept ways that when the number of lessons is 0, Marjorie loses $250.

    This figure shows the graph of a straight line on the x y-coordinate plane. The x-axis runs from negative 4 to 28. The y-axis runs from negative 250 to 450. The line goes through the points (0, negative 250) and (20, 450).

    Use Slopes to Identify Parallel and Perpendicular Lines

    In the following exercises, employ slopes and \(y\)-intercepts to determine if the lines are parallel, perpendicular, or neither.

    60. \(4x−3y=−1;\quad y=43x−3\)

    61. \(y=5x−ane;\quad 10x+2y=0\)

    Answer

    neither

    62. \(3x−2y=five;\quad 2x+3y=six\)

    63. \(2x−y=viii;\quad x−2y=iv\)

    Answer

    not parallel

    Find the Equation of a Line

    Find an Equation of the Line Given the Gradient and y-Intercept

    In the post-obit exercises, detect the equation of a line with given gradient and y-intercept. Write the equation in slope–intercept form.

    64. Slope \(\frac{1}{3}\) and \(y\)-intercept \((0,−6)\)

    65. Slope \(−5\) and \(y\)-intercept \((0,−3)\)

    Answer

    \(y=−5x−3\)

    66. Gradient \(0\) and \(y\)-intercept \((0,4)\)

    67. Slope \(−2\) and \(y\)-intercept \((0,0)\)

    Answer

    \(y=−2x\)

    In the following exercises, find the equation of the line shown in each graph. Write the equation in slope–intercept form.

    68.
    This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 1), (1, 3), and (2, 5).

    69.
    This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, 5), (1, 2), and (2, negative 1).

    Answer

    \(y=−3x+5\)

    seventy.
    This figure has a graph of a straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 2), (4, 1), and (8, 4).

    71.
    This figure has a graph of a horizontal straight line on the x y-coordinate plane. The x and y-axes run from negative 10 to 10. The line goes through the points (0, negative 4), (1, negative 4), and (2, negative 4).

    Answer

    \(y=−4\)

    Observe an Equation of the Line Given the Slope and a Bespeak

    In the post-obit exercises, find the equation of a line with given slope and containing the given point. Write the equation in slope–intercept form.

    72. \(grand=−\frac{1}{4}\), point \((−8,3)\)

    73. \(grand=\frac{3}{5}\), point \((10,6)\)

    Answer

    \(y=\frac{three}{v}x\)

    74. Horizontal line containing \((−2,seven)\)

    75. \(m=−2\), point \((−i,−three)\)

    Answer

    \(y=−2x−v\)

    Find an Equation of the Line Given Two Points

    In the post-obit exercises, notice the equation of a line containing the given points. Write the equation in slope–intercept form.

    76. \((2,10)\) and \((−2,−2)\)

    77. \((7,ane)\) and \((5,0)\)

    Reply

    \(y=\frac{i}{2}x−\frac{5}{2}\)

    78. \((3,viii)\) and \((three,−4)\)

    79. \((v,2)\) and \((−1,2)\)

    Answer

    \(y=2\)

    Discover an Equation of a Line Parallel to a Given Line

    In the following exercises, observe an equation of a line parallel to the given line and contains the given indicate. Write the equation in slope–intercept course.

    80. line \(y=−3x+six\), betoken \((1,−5)\)

    81. line \(2x+5y=−10\), indicate \((10,4)\)

    Respond

    \(y=−\frac{2}{5}x+8\)

    82. line \(x=4\), point \((−2,−1)\)

    83. line \(y=−five\), point \((−four,3)\)

    Answer

    \(y=3\)

    Find an Equation of a Line Perpendicular to a Given Line

    In the following exercises, find an equation of a line perpendicular to the given line and contains the given signal. Write the equation in slope–intercept form.

    84. line \(y=−\frac{four}{5}ten+2\), indicate \((8,9)\)

    85. line \(2x−3y=nine\), point \((−4,0)\)

    Answer

    \(y=−\frac{3}{2}x−6\)

    86. line \(y=3\), point \((−1,−3)\)

    87. line \(10=−v\) point \((ii,1)\)

    Answer

    \(y=one\)

    Graph Linear Inequalities in Two Variables

    Verify Solutions to an Inequality in Two Variables

    In the following exercises, determine whether each ordered pair is a solution to the given inequality.

    88. Determine whether each ordered pair is a solution to the inequality \(y<10−3\):

    ⓐ \((0,1)\) ⓑ \((−two,−4)\) ⓒ \((five,2)\) ⓓ \((3,−1)\)
    ⓔ \((−i,−v)\)

    89. Determine whether each ordered pair is a solution to the inequality \(x+y>4\):

    ⓐ \((half-dozen,ane)\) ⓑ \((−iii,vi)\) ⓒ \((three,ii)\) ⓓ \((−5,ten)\) ⓔ \((0,0)\)

    Answer

    Recognize the Relation Betwixt the Solutions of an Inequality and its Graph

    In the post-obit exercises, write the inequality shown by the shaded region.

    90. Write the inequality shown by the graph with the boundary line \(y=−x+2.\)

    This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, 2), (1, 1), and (2, 0). The line divides the x y-coordinate plane into two halves. The line and the bottom left half are shaded red to indicate that this is where the solutions of the inequality are.

    91. Write the inequality shown by the graph with the boundary line \(y=\frac{two}{3}ten−3\).

    This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 3), (3, negative 1), and (6, 1). The line divides the x y-coordinate plane into two halves. The line and the top left half are shaded red to indicate that this is where the solutions of the inequality are.

    Answer

    \(y>\frac{ii}{iii}ten−3\)

    92. Write the inequality shown past the shaded region in the graph with the boundary line \(10+y=−4\).

    This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 4), (negative 2, negative 2), and (negative 4, 0). The line divides the x y-coordinate plane into two halves. The line and the top right half are shaded red to indicate that this is where the solutions of the inequality are.

    93. Write the inequality shown past the shaded region in the graph with the purlieus line \(ten−2y=six\).

    This figure has the graph of a straight line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A line is drawn through the points (0, negative 3), (2, negative 2), and (6, 0). The line divides the x y-coordinate plane into two halves. The line and the bottom right half are shaded red to indicate that this is where the solutions of the inequality are.

    Answer

    \(ten−2y\geq 6\)

    Graph Linear Inequalities in Two Variables

    In the following exercises, graph each linear inequality.

    94. Graph the linear inequality \(y>\frac{2}{5}10−4\).

    95. Graph the linear inequality \(y\leq −\frac{1}{iv}x+three\).

    Answer

    This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 3), (4, 2), and (8, 1). The line divides the x y-coordinate plane into two halves. The bottom left half is shaded red to indicate that this is where the solutions of the inequality are.

    96. Graph the linear inequality \(10−y\leq 5\).

    97. Graph the linear inequality \(3x+2y>10.\)

    Respond

    This figure has the graph of a straight dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 5), (2, 2), and (4, negative 1). The line divides the x y-coordinate plane into two halves. The top right half is shaded red to indicate that this is where the solutions of the inequality are.

    98. Graph the linear inequality \(y\leq −3x\).

    99. Graph the linear inequality \(y<half dozen.\)

    Answer

    This figure has the graph of a straight horizontal dashed line on the x y-coordinate plane. The x and y axes run from negative 10 to 10. A straight dashed line is drawn through the points (0, 6), (1, 6), and (2, 6). The line divides the x y-coordinate plane into two halves. The bottom half is shaded red to indicate that this is where the solutions of the inequality are.

    Solve Applications using Linear Inequalities in Ii Variables

    100. Shanthie needs to earn at least $500 a calendar week during her summertime break to pay for college. She works two jobs. One equally a swimming teacher that pays $x an 60 minutes and the other as an intern in a police force office for $25 hour. How many hours does Shanthie demand to piece of work at each job to earn at least $500 per week?

    ⓐ Let 10 exist the number of hours she works didactics pond and let y be the number of hours she works as an intern. Write an inequality that would model this situation.
    ⓑ Graph the inequality.
    ⓒ Find three ordered pairs \((x,y)\) that would exist solutions to the inequality. And so, explain what that means for Shanthie.

    101. Atsushi he needs to exercise enough to burn \(600\) calories each day. He prefers to either run or bike and burns \(20\) calories per minute while running and \(15\) calories a infinitesimal while biking.

    ⓐ If 10 is the number of minutes that Atsushi runs and y is the number minutes he bikes, find the inequality that models the situation.
    ⓑ Graph the inequality.
    ⓒ List three solutions to the inequality. What options do the solutions provide Atsushi?

    Answer

    ⓐ \(20x+15y\geq 60020x+15y\geq 600\)

    The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from 0 to 50. The y-axis runs from 0 to 50. The line goes through the points (0, 40) and (30, 0). The line divides the coordinate plane into two halves. The top right half and the line are colored red to indicate that this is the solution set.

    ⓒ Answers will vary.

    Relations and Functions

    Detect the Domain and Range of a Relation

    In the post-obit exercises, for each relation, ⓐ detect the domain of the relation ⓑ find the range of the relation.

    102. \({\{(five,−2),\,(5,−iv),\,(7,−vi),\,(8,−8),\,(9,−x)}\}\)

    103. \({\{(−iii,7),\,(−2,3),\,(−i,nine), \,(0,−3),\,(−one,8)}\}\)

    Answer

    ⓐ \(D: {−3, −ii, −1, 0}\)
    ⓑ \(R: {7, 3, 9, −iii, 8}\)

    In the post-obit exercise, utilise the mapping of the relation to ⓐ listing the ordered pairs of the relation ⓑ find the domain of the relation ⓒ find the range of the relation.

    104. The mapping below shows the average weight of a kid according to age.

    This figure shows two table that each have one column. The table on the left has the header

    In the post-obit practice, use the graph of the relation to ⓐ list the ordered pairs of the relation ⓑ find the domain of the relation ⓒ observe the range of the relation.

    105.
    The figure shows the graph of some points on the x y-coordinate plane. The x and y-axes run from negative 6 to 6. The points (negative 3, 1), (negative 2, negative 1), (negative 2, negative 3), (0, negative 1), (0, 4), and (4, 3).

    Answer

    ⓐ \((iv, 3), \,(−2, −3), \,(−2, −one), \,(−3, i), \,(0, −ane), \,(0, 4)\)
    ⓑ \(D: {−3, −2, 0, iv}\)
    ⓒ \(R: {−three, −1, ane, 3, iv}\)

    Determine if a Relation is a Function

    In the following exercises, apply the set of ordered pairs to ⓐ decide whether the relation is a function ⓑ find the domain of the relation ⓒ find the range of the relation.

    106. \({\{(9,−five),\,(4,−3),\,(1,−i),\,(0,0),\,(1,ane),\,(iv,3),\,(ix,v)}\}\)

    107. \({\{(−3,27),\,(−2,8),\,(−1,one),\,(0,0),\,(1,1),\,(two,viii),\,(iii,27)}\}\)

    Respond

    ⓐ yes ⓑ \({−3, −2, −1, 0, 1, 2, 3}\)
    ⓒ \({0, 1, viii, 27}\)

    In the post-obit exercises, use the mapping to ⓐ determine whether the relation is a function ⓑ find the domain of the office ⓒfind the range of the function.

    108.
    This figure shows two table that each have one column. The table on the left has the header

    109.
    This figure shows two table that each have one column. The table on the left has the header

    Answer

    ⓐ \({−3, −2, −1, 0, 1, 2, iii}\)
    ⓑ \({−three, −ii, −1, 0, 1, 2, 3}\)
    ⓒ \({−243, −32, −1, 0, 1, 32, 243}\)

    In the following exercises, decide whether each equation is a part.

    110. \(2x+y=−3\)

    111. \(y=ten^2\)

    Answer

    yes

    112. \(y=3x−five\)

    113. \(y=x^3\)

    Answer

    aye

    114. \(2x+y2=4\)

    Find the Value of a Part

    In the following exercises, evaluate the function:

    ⓐ \(f(−2)\) ⓑ \(f(3)\) ⓒ \(f(a)\).

    115. \(f(x)=3x−four\)

    Answer

    ⓐ \(f(−2)=−10\) ⓑ \(f(three)=5\) ⓒ \(f(a)=3a−4\)

    116. \(f(x)=−2x+5\)

    117. \(f(ten)=x^2−5x+6\)

    Answer

    ⓐ \(f(−2)=20\) ⓑ \(f(3)=0\) ⓒ \(f(a)=a^2−5a+6\)

    118. \(f(10)=3x^ii−2x+ane\)

    In the following exercises, evaluate the office.

    119. \(g(x)=3x2−5x;\space g(ii)\)

    Reply

    \(2\)

    120. \(F(x)=2x2−3x+1;\infinite F(−1)\)

    121. \(h(t)=iv|t−1|+2;\infinite h(t)=iv\)

    Reply

    \(18\)

    122. \(f(x)=x+2x−one;\space f(3)\)

    Graphs of Functions

    Utilize the Vertical line Test

    In the following exercises, decide whether each graph is the graph of a function.

    123.
    The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 5), (negative 1, 2), (0, 1), (1, 2), and (2, 5). The lowest point on the graph is (0, 1).

    Answer

    yes

    124.
    The figure has an s-shaped function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curve goes through the points (negative 1, negative 1), (0, 0), and (1, 1).

    125.
    The figure has a circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The circle goes through the points (negative 5, 0), (5, 0), (0, negative 5), and (0, 5).

    Reply

    no

    126.
    The figure has a parabola opening to the right graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 0), (negative 1, 1), (negative 1, negative 1), (2, 2), and (2, negative 2). The left-most point on the graph is (negative 2, 0).

    127.
    The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, negative 1), (0, 0), and (1, 1).

    Answer

    yes

    128.
    The figure has two curved lines graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line on the left goes through the points (negative 3, 0), (negative 4, 2), and (negative 4, negative 2). The curved line on the right goes through the points (3, 0), (4, 2), and (4, negative 2).

    129.
    The figure has a sideways absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line bends at the point (0, negative 1) and goes to the right. The line goes through the points (1, 0), (1, negative 2), (2, 1), and (2, negative 3).

    Answer

    no

    Place Graphs of Basic Functions

    In the following exercises, ⓐ graph each part ⓑ state its domain and range. Write the domain and range in interval notation.

    130. \(f(x)=5x+1\)

    131. \(f(10)=−4x−ii\)

    Answer

    The figure has a linear function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The line goes through the points (negative 2, 6), (negative 1, 2), and (0, negative 2).

    ⓑ \(D: (-\inf ,\inf ), R: (-\inf ,\inf )\)

    132. \(f(x)=\frac{2}{3}x−i\)

    133. \(f(x)=−6\)

    Answer

    The figure has a constant function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 8 to 4. The line goes through the points (0, negative 6), (1, negative 6), and (2, negative 6).

    ⓑ \(D: (-\inf ,\inf ), R: (-\inf ,\inf )\)

    134. \(f(x)=2x\)

    135. \(f(x)=3x^2\)

    Answer

    The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 1, 3), (0, 0), and (1, 3). The lowest point on the graph is (0, 0).

    ⓑ \(D: (-\inf ,\inf ), R: (-\inf ,0]\)

    136. \(f(ten)=−12x^2\)

    137. \(f(10)=x^ii+ii\)

    Reply

    The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 4 to 8. The parabola goes through the points (negative 2, 6), (negative 1, 3), (0, 2), (1, 3), and (2, 6). The lowest point on the graph is (0, 2).

    ⓑ \(D: (-\inf ,\inf ), R: (-\inf ,\inf )\)

    138. \(f(ten)=10^3−ii\)

    139. \(f(x)=\sqrt{x+2}\)

    Answer

    The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from negative 4 to 8. The y-axis runs from negative 2 to 10. The half-line starts at the point (negative 2, 0) and goes through the points (negative 1, 1) and (2, 2).

    ⓑ \(D: [−2,−2, \inf ), \infinite R: [0,\inf )\)

    140. \(f(ten)=−|10|\)

    141. \(f(x)=|10|+one\)

    Answer

    The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 1). The line goes through the points (negative 1, 2) and (1, 2).

    ⓑ \(D: (-\inf ,\inf ), \space R: [1,\inf )\)

    Read Information from a Graph of a Function

    In the following exercises, utilize the graph of the role to discover its domain and range. Write the domain and range in interval annotation

    142.
    The figure has a square root function graphed on the x y-coordinate plane. The x-axis runs from 0 to 10. The y-axis runs from 0 to 10. The half-line starts at the point (1, 0) and goes through the points (2, 1) and (5, 2).

    143.
    The figure has an absolute value function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The vertex is at the point (0, 2). The line goes through the points (negative 1, 3) and (1, 3).

    Answer

    \(D: (-\inf ,\inf ), R: [2,\inf )\)

    144.
    The figure has a cubic function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 2, negative 4), (0, 0), and (2, 4).

    In the post-obit exercises, use the graph of the office to find the indicated values.

    145.
    This figure has a wavy curved line graphed on the x y-coordinate plane. The x-axis runs from negative 2 times pi to 2 times pi. The y-axis runs from negative 6 to 6. The curved line segment goes through the points (negative 2 times pi, 0), (negative 3 divided by 2 times pi, 1), (negative pi, 0), (negative 1 divided by 2 times pi, negative 1), (0, 0), (1 divided by 2 times pi, 1), (pi, 0), (3 divided by 2 times pi, negative 1), and (2 times pi, 0). The points (negative 3 divided by 2 times pi, 1) and (1 divided by 2 times pi, 1) are the highest points on the graph. The points (negative 1 divided by 2 times pi, negative 1) and (3 divided by 2 times pi, negative 1) are the lowest points on the graph. The pattern extends infinitely to the left and right.

    ⓐ Find \(f(0)\).
    ⓑ Find \(f(12\pi )\).
    ⓒ Find \(f(−32\pi )\).
    ⓓ Find the values for \(x\) when \(f(x)=0\).
    ⓔ Detect the \(x\)-intercepts.
    ⓕ Observe the \(y\)-intercept(south).
    ⓖ Find the domain. Write information technology in interval annotation.
    ⓗ Find the range. Write it in interval annotation.

    Answer

    ⓐ \(f(x)=0\) ⓑ \(f(\pi /2)=one\)
    ⓒ \(f(−three\pi /2)=1\) ⓓ \(f(x)=0\) for \(x=−2\pi ,−\pi ,0,\pi ,2\pi\)
    ⓔ \((−two\pi ,0), (−\pi ,0), (0,0), (\pi ,0), (2\pi ,0)\) ⓕ \((0,0)\)
    ⓖ \([−ii\pi ,2\pi ]\) ⓗ \([−1,ane]\)

    146.
    The figure has a half-circle graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line segment starts at the point (negative 2, 0). The line goes through the point (0, 2) and ends at the point (2, 0). The point (0, 2) is the highest point on the graph.

    ⓐ Discover \(f(0)\).
    ⓑ Find the values for \(x\) when \(f(10)=0\).
    ⓒ Find the \(x\)-intercepts.
    ⓓ Notice the \(y\)-intercept(southward).
    ⓔ Find the domain. Write information technology in interval note.
    ⓕ Notice the range. Write it in interval notation.

    Practice Exam

    1. Plot each point in a rectangular coordinate organisation.

    ⓐ \((two,five)\)
    ⓑ \((−i,−3)\)
    ⓒ \((0,ii)\)
    ⓓ \((−iv,32)\)
    ⓔ \((5,0)\)

    Answer

    This figure shows points plotted on the x y-coordinate plane. The x and y axes run from negative 10 to 10. The point labeled a is 2 units to the right of the origin and 5 units above the origin and is located in quadrant I. The point labeled b is 1 unit to the left of the origin and 3 units below the origin and is located in quadrant III. The point labeled c is 2 units above the origin and is located on the y-axis. The point labeled d is 4 units to the left of the origin and 1.5 units above the origin and is located in quadrant II. The point labeled e is 5 units to the right of the origin and is located on the x-axis.

    2. Which of the given ordered pairs are solutions to the equation \(3x−y=6\)?

    ⓐ \((3,3)\) ⓑ \((2,0)\) ⓒ \((four,−vi)\)

    iii. Observe the slope of each line shown.

    The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 5, 2) (0, negative 1), and (5, negative 4).

    The figure has a straight vertical line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (2, 0) (2, negative 1), and (2, 1).

    Answer

    ⓐ \(−\frac{3}{5}\) ⓑ undefined

    iv. Notice the slope of the line between the points \((5,2)\) and \((−1,−4)\).

    5. Graph the line with slope \(\frac{1}{2}\) containing the point \((−3,−four)\).

    Answer

    The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, negative 4) (negative 1, negative 3), and (1, negative 2).

    6. Find the intercepts of \(4x+2y=−8\) and graph.

    Graph the line for each of the following equations.

    7. \(y=\frac{5}{3}x−ane\)

    Answer

    The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, negative 6) (0, negative 1), and (3, 4).

    eight. \(y=−ten\)

    nine. \(y=ii\)

    Answer

    The figure has a straight horizontal line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 1, 2) (0, 2), and (1, 2).

    Find the equation of each line. Write the equation in slope-intercept form.

    10. slope \(−\frac{3}{4}\) and \(y\)-intercept \((0,−ii)\)

    xi. \(chiliad=2\), point \((−three,−1)\)

    Reply

    \(y=2x+5\)

    12. containing \((10,ane)\) and \((6,−1)\)

    xiii. perpendicular to the line \(y=\frac{five}{4}x+2\), containing the point \((−10,3)\)

    Answer

    \(y=−\frac{4}{5}10−5\)

    14. Write the inequality shown by the graph with the purlieus line \(y=−x−3\).

    The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 3, 0), (0, negative 3), and (1, negative 4). The line divides the coordinate plane into two halves. The bottom left half and the line are colored red to indicate that this is the solution set.

    Graph each linear inequality.

    15. \(y>\frac{3}{2}ten+5\)

    Answer

    The figure has a straight dashed line graphed on the x y-coordinate plane. The x-axis runs from negative 10 to 10. The y-axis runs from negative 10 to 10. The line goes through the points (negative 2, 2), (0, 5), and (2, 8). The line divides the coordinate plane into two halves. The top left half is colored red to indicate that this is the solution set.

    sixteen. \(x−y\geq −4\)

    17. \(y\leq −5x\)

    Answer

    The figure has a straight line graphed on the x y-coordinate plane. The x-axis runs from negative 8 to 8. The y-axis runs from negative 8 to 8. The line goes through the points (negative 1, 5), (0, 0), and (1, negative 5). The line divides the coordinate plane into two halves. The bottom left half and the line are colored red to indicate that this is the solution set.

    18. Hiro works ii office time jobs in order to earn enough money to meet her obligations of at least $450 a week. Her chore at the mall pays $x an hour and her administrative assistant job on campus pays $xv an hr. How many hours does Hiro need to work at each task to earn at least $450?

    ⓐ Permit x exist the number of hours she works at the mall and let y be the number of hours she works every bit administrative banana. Write an inequality that would model this situation.
    ⓑ Graph the inequality .
    ⓒ Find three ordered pairs \((10,y)\) that would be solutions to the inequality. Then explain what that means for Hiro.

    19. Use the set of ordered pairs to ⓐ determine whether the relation is a part, ⓑ find the domain of the relation, and ⓒnotice the range of the relation.

    \({\{(−3,27),(−2,8),(−ane,one),(0,0),
    (i,1),(2,8),(3,27)}\}\)

    Answer

    ⓐ yes ⓑ \({\{−three,−2,−1,0,1,2,three}\}\) ⓒ \({\{0, 1, eight, 27}\}\)

    twenty. Evaluate the role: ⓐ \(f(−i)\) ⓑ \(f(2)\) ⓒ \(f(c)\).

    \(f(ten)=4x^2−2x−3\)

    22. Determine whether the graph is the graph of a function. Explain your answer.

    The figure has a cube function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The curved line goes through the points (negative 1, 1), (0, 2), and (1, 3).

    In the following exercises, ⓐ graph each function ⓑ state its domain and range.
    Write the domain and range in interval notation.

    23. \(f(x)=x^two+1\)

    Answer

    The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 2 to 10. The parabola goes through the points (negative 2, 5), (negative 1, 2), (0, 1), (1, 2), and (2, 5). The lowest point on the graph is (0, 1).

    ⓑ \(D: (-\inf ,\inf ), R: [1,\inf )\)

    24. \(f(10)=\sqrt{x+one}\)

    The figure has a square function graphed on the x y-coordinate plane. The x-axis runs from negative 6 to 6. The y-axis runs from negative 6 to 6. The parabola goes through the points (negative 2, 0), (negative 1, negative 3), (0, negative 4), (1, negative 3), and (2, 0). The lowest point on the graph is (0, negative 4).

    ⓑ Find the \(y\)-intercepts.
    ⓒ Find \(f(−i)\).
    ⓓ Find \(f(1)\).
    ⓔ Discover the domain. Write information technology in interval notation.
    ⓕ Find the range. Write it in interval annotation.

    Answer

    ⓐ \(x=−2,2\) ⓑ \(y=−4\)
    ⓒ \(f(−1)=−3\) ⓓ \(f(1)=−iii\)
    ⓔ \(D: (-\inf ,\inf )\) ⓕ \(R: [−four, \inf)\)

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    Source: https://math.libretexts.org/Bookshelves/Algebra/Intermediate_Algebra_%28OpenStax%29/03:_Graphs_and_Functions/3.0E:_3.E:_Chapter_Exercises

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