Solved: In Exercises 85 and 86, find an equation of the graph that consists of all

In Exercises 14, match the equation with its graph. [Graphs are labeled (a), (b), (c), and (d).]y
1 2 x 2 x

In Exercises 14, match the equation with its graph. [Graphs are labeled (a), (b), (c), and (d).]y
9 x2 y

In Exercises 14, match the equation with its graph. [Graphs are labeled (a), (b), (c), and (d).]y
4 x 3 x 2 y

In Exercises 14, match the equation with its graph. [Graphs are labeled (a), (b), (c), and (d).]

In Exercises 5–14, sketch the graph of the equation by point plotting. \(y=\frac{3}{2} x+1\) Equation Transcription: Text Transcription: y=3/2x+1

In Exercises 5–14, sketch the graph of the equation by point plotting. \(y=6-2x\) Equation Transcription: Text Transcription: y=6-2x

In Exercises 514, sketch the graph of the equation by point plotting.y
4 x2

In Exercises 5–14, sketch the graph of the equation by point plotting. \(y=(x-3)^{2}\) Equation Transcription: Text Transcription: y=(x-3)^2

In Exercises 5–14, sketch the graph of the equation by point plotting. \(y=|x+2|\) Equation Transcription: Text Transcription: y=|x+2|

In Exercises 5–14, sketch the graph of the equation by point plotting. \(y=|x|-1\) Equation Transcription: Text Transcription: y=|x|-1

In Exercises 5–14, sketch the graph of the equation by point plotting. \(y=\sqrt{x}-4\) Equation Transcription: Text Transcription: y=sqrt x-4

In Exercises 514, sketch the graph of the equation by point plotting.y
x 2 y

In Exercises 5–14, sketch the graph of the equation by point plotting. \(y=\frac{2}{x}\) Equation Transcription: Text Transcription: y=2/x

In Exercises 514, sketch the graph of the equation by point plotting.y
1 x 1 y

In Exercises 15 and 16, describe the viewing window that yields the figure. \(y=x^{3}-3 x^{2}+4\) Equation Transcription: Text Transcription: y=x^3-3x^2+4

In Exercises 15 and 16, describe the viewing window that yields the figure. \(y=|x|+|x-10|\) Equation Transcription: Text Transcription: y=|x|+|x-10|

In Exercises 17 and 18, use a graphing utility to graph the equation. Move the cursor along the curve to approximate the unknown coordinate of each solution point accurate to two decimal places.y
5 x
2, y
x, 3 y

In Exercises 17 and 18, use a graphing utility to graph the equation. Move the cursor along the curve to approximate the unknown coordinate of each solution point accurate to two decimal places.y
x
0.5, y
x, 4 5 5

In Exercises 19–26, find any intercepts. \(y=x^{2}+x-2\) Equation Transcription: Text Transcription: y=x^2+x-2

In Exercises 19–26, find any intercepts. \(y^{2}=x^{3}-4 x\) Equation Transcription: Text Transcription: y^2=x^3-4x

In Exercises 1926, find any interceptsy

x 1x y
x 2 1 225

In Exercises 19–26, find any intercepts. \(y=(x-1) \sqrt{x^{2}+1}\) Equation Transcription: Text Transcription: y=(x-1)sqrt x^2+1

In Exercises 1926, find any interceptsy
3
2 x x

In Exercises 19–26, find any intercepts. \(y=\frac{x^{2}+3 x}{(3 x+1)^{2}}\) Equation Transcription: Text Transcription: y=x^2+3x/(3x+1)^2

In Exercises 19–26, find any intercepts. \(x^{2} y-x^{2}+4 y=0\) Equation Transcription: Text Transcription: x^2y-x^2+4y=0

In Exercises 1926, find any interceptsy
2x x x 2 1 2

In Exercises 2738, test for symmetry with respect to each axis and to the origin.y
x 2 x 2 2 y

In Exercises 2738, test for symmetry with respect to each axis and to the origin.y
x y
x 2 x 2

In Exercises 27–38, test for symmetry with respect to each axis and to the origin. \(y^{2}=x^{3}-4 x\) Equation Transcription: Text Transcription: y^2=x^3-4x

In Exercises 27–38, test for symmetry with respect to each axis and to the origin. \(y=x^{3}+x\) Equation Transcription: Text Transcription: y=x^3+x

In Exercises 2738, test for symmetry with respect to each axis and to the origin.y
4

In Exercises 27–38, test for symmetry with respect to each axis and to the origin. \(x y^{2}=-10\) Equation Transcription: Text Transcription: xy^2=-10

In Exercises 27–38, test for symmetry with respect to each axis and to the origin. \(y=4-\sqrt{x+3}\) Equation Transcription: Text Transcription: y=4-sqrt x+3

In Exercises 2738, test for symmetry with respect to each axis and to the origin.xy 4 x y
4 x 3 2
0 xy xy

In Exercises 2738, test for symmetry with respect to each axis and to the origin.y
x x2 1

In Exercises 2738, test for symmetry with respect to each axis and to the origin.y
x2 x2 1 y

In Exercises 27–38, test for symmetry with respect to each axis and to the origin. \(y=\left|x^{3}+x\right|\) Equation Transcription: Text Transcription: y=|x^3+x|

In Exercises 27–38, test for symmetry with respect to each axis and to the origin. \(|y|-x=3\) Equation Transcription: Text Transcription: |y|-x=3

In Exercises 3956, sketch the graph of the equation. Identify any intercepts and test for symmetry.y
3x 2 x

In Exercises 39–56, sketch the graph of the equation. Identify any intercepts and test for symmetry. \(y=-\frac{1}{2} x+2\) Equation Transcription: Text Transcription: y=-1/2x+2

In Exercises 39–56, sketch the graph of the equation. Identify any intercepts and test for symmetry. \(y=\frac{1}{2} x-4\) Equation Transcription: Text Transcription: y=1/2x-4

In Exercises 3956, sketch the graph of the equation. Identify any intercepts and test for symmetry.y
2 3 y
x 1 1

In Exercises 39–56, sketch the graph of the equation. Identify any intercepts and test for symmetry. \(y=1-x^{2}\) Equation Transcription: Text Transcription: y=1-x^2

In Exercises 39–56, sketch the graph of the equation. Identify any intercepts and test for symmetry. \(y=x^{2}+3\) Equation Transcription: Text Transcription: y=x^2+3

In Exercises 3956, sketch the graph of the equation. Identify any intercepts and test for symmetry.y

x 3 2 x 2 y

In Exercises 39–56, sketch the graph of the equation. Identify any intercepts and test for symmetry. \(y=2 x^{2}+x\) Equation Transcription: Text Transcription: y=2x^2+x

In Exercises 39–56, sketch the graph of the equation. Identify any intercepts and test for symmetry. \(y=x^{3}+2\) Equation Transcription: Text Transcription: y=x^3+2

In Exercises 3956, sketch the graph of the equation. Identify any intercepts and test for symmetry.y
x y
x 3 4x 3

In Exercises 39–56, sketch the graph of the equation. Identify any intercepts and test for symmetry. \(y=x \sqrt{x+2}\) Equation Transcription: Text Transcription: y=x sqrt x+2

In Exercises 39–56, sketch the graph of the equation. Identify any intercepts and test for symmetry. \(y=\sqrt{9-x^{2}}\) Equation Transcription: Text Transcription: y=sqrt 9-x^2

In Exercises 3956, sketch the graph of the equation. Identify any intercepts and test for symmetry.x
y 2 4 3 y

In Exercises 39–56, sketch the graph of the equation. Identify any intercepts and test for symmetry. \(x=y^{2}-4\) Equation Transcription: Text Transcription: x=y^2-4

In Exercises 39–56, sketch the graph of the equation. Identify any intercepts and test for symmetry. \(y=\frac{1}{x}\) Equation Transcription: Text Transcription: y=1/x

In Exercises 3956, sketch the graph of the equation. Identify any intercepts and test for symmetry.y
10 x2 1 y

In Exercises 3956, sketch the graph of the equation. Identify any intercepts and test for symmetry.y
6 x

In Exercises 3956, sketch the graph of the equation. Identify any intercepts and test for symmetry.y
6 x

In Exercises 5760, use a graphing utility to graph the equation. Identify any intercepts and test for symmetry.y 2
4 2 x
9

In Exercises 5760, use a graphing utility to graph the equation. Identify any intercepts and test for symmetry.x2 4y y 2
4 2

In Exercises 5760, use a graphing utility to graph the equation. Identify any intercepts and test for symmetry.x 3y 2
8 2
6

In Exercises 5760, use a graphing utility to graph the equation. Identify any intercepts and test for symmetry.3x 4y x 3y 2
8 2

In Exercises 6168, find the point(s) of intersection of the graphs of the equations.x y
2 22x y
1 5

In Exercises 6168, find the point(s) of intersection of the graphs of the equations.2x 3y
13 35x 3y
1

In Exercises 6168, find the point(s) of intersection of the graphs of the equations.x2 y
6 x y
4

In Exercises 6168, find the point(s) of intersection of the graphs of the equations.x
3 y2 xy
x 1 x

In Exercises 6168, find the point(s) of intersection of the graphs of the equations.x 2
25 2 y2
5 x y
1 2

In Exercises 61–68, find the point(s) of intersection of the graphs of the equations. \(\begin{array}{l} x^{2}+y^{2}=25 \\ 2 x+y=10 \end{array} \) Equation Transcription: Text Transcription: x^2+y^2=25 2x+y=10

In Exercises 61–68, find the point(s) of intersection of the graphs of the equations. \(\begin{array}{l} y=x^{3} \\ y=x \end{array} \) Equation Transcription: Text Transcription: y=x^3 y=x

In Exercises 61–68, find the point(s) of intersection of the graphs of the equations. \(\begin{array}{l} y=x^{3}-4 x \\ y=-(x+2) \end{array} \) Equation Transcription: Text Transcription: y=x^3-4x y=-(x+2)

In Exercises 6972, use a graphing utility to find the point(s) of intersection of the graphs. Check your results analyticallyy
x 2 1 3 2x2 x 1 y
x2 3x 1 y y

In Exercises 6972, use a graphing utility to find the point(s) of intersection of the graphs. Check your results analyticallyy
x4 2x y
x 2 1 3 y
1 x2 y

In Exercises 6972, use a graphing utility to find the point(s) of intersection of the graphs. Check your results analyticallyy
x 6 y y
x y
6 x 2 4x y

In Exercises 6972, use a graphing utility to find the point(s) of intersection of the graphs. Check your results analyticallyy
2x 3 6 y y
6 x 2

Modeling Data The table shows the Consumer Price Index (CPI) for selected years. (Source: Bureau of Labor Statistics) (a) Use the regression capabilities of a graphing utility to find a mathematical model of the form for the data. In the model, represents the CPI and represents the year, with corresponding to 1970. (b) Use a graphing utility to plot the data and graph the model. Compare the data with the model. (c) Use the model to predict the CPI for the year 2010.

Modeling Data The table shows the average number of acres per farm in the United States for selected years. (Source: U.S. Department of Agriculture) (a) Use the regression capabilities of a graphing utility to find a mathematical model of the form for the data. In the model, represents the average acreage and represents the year, with corresponding to 1950. (b) Use a graphing utility to plot the data and graph the model. Compare the data with the model. (c) Use the model to predict the average number of acres per farm in the United States in the year 2010.

Break-Even Point Find the sales necessary to break even if the cost of producing units is Cost equation and the revenue for selling units is Revenue equation

Copper Wire The resistance in ohms of 1000 feet of solid copper wire at can be approximated by the modelwhere is the diameter of the wire in mils (0.001 inch). Use a graphing utility to graph the model. If the diameter of the wire is doubled, the resistance is changed by about what factor?

In Exercises 77 and 78, write an equation whose graph has the indicated property. (There may be more than one correct answer.) The graph has intercepts at and \(x=-2, x=4, \text { and } x=6\). Equation Transcription: Text Transcription: x=-2, x=4, and x=6

In Exercises 77 and 78, write an equation whose graph has the indicated property. (There may be more than one correct answer.) The graph has intercepts at and \(x=-\frac{5}{2}, x=2, \text { and } x=\frac{3}{2}\). Equation Transcription: Text Transcription: x=-5/2, x=2, and x=3/2

Each table shows solution points for one of the following equations. (i) (ii) (iii) (iv) Match each equation with the correct table and find Explain your reasoning.

(a) Prove that if a graph is symmetric with respect to the -axis and to the -axis, then it is symmetric with respect to the origin. Give an example to show that the converse is not true. (b) Prove that if a graph is symmetric with respect to one axis and to the origin, then it is symmetric with respect to the other axis.

True or False? In Exercises 81–84, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If (1, -2) is a point on a graph that is symmetric with respect to the x-axis, then (-1, -2) is also a point on the graph.

True or False? In Exercises 81–84, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If (1, -2) is a point on a graph that is symmetric with respect to the y-axis, then (-1, -2) is also a point on the graph.

True or False? In Exercises 8184, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If and then the graph of has two -intercepts.

True or False? In Exercises 8184, determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false.If and then the graph of has only one -intercept.

In Exercises 85 and 86, find an equation of the graph that consists of all points having the given distance from the origin. (For a review of the Distance Formula, see Appendix D.)The distance from the origin is twice the distance from
0, 3.

In Exercises 85 and 86, find an equation of the graph that consists of all points having the given distance from the origin. (For a review of the Distance Formula, see Appendix D.)The distance from the origin is times the distance from
2, 0.