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Graphs

Precalculus Enhanced with Graphing Utilities · 513 exercises

Q. 28

Plot each point. Then plot the point that is symmetric to it with respect to -

(a) the x-axis

(b) the y-axis

(c) the origin

Point (-1, -1)

9 step solution

Q. 29

Plot each point. Then plot the point that is symmetric to it with respect to -

(a) the x-axis

(b) the y-axis

(c) the origin

Point (-3, -4)

9 step solution

Q. 30

Plot each point. Then plot the point that is symmetric to it with respect to -

(a) the x-axis

(b) the y-axis

(c) the origin

Point (4, 0)

9 step solution

Q. 31

Plot each point. Then plot the point that is symmetric to it with respect to -

(a) the x-axis

(b) the y-axis

(c) the origin

Point (0, -3)

9 step solution

Q. 32

Plot each point. Then plot the point that is symmetric to it with respect to -

(a) the x-axis

(b) the y-axis

(c) the origin

Point (-3, 0)

9 step solution

Q. 33

The graph of an equation is given.

(a). Find the intercepts.

(b). Indicate whether the graph is symmetric with respect to

the x-axis, the y-axis, or the origin.

6 step solution

Q. 34

The graph of an equation is given.

(a). Find the intercepts.

(b). Indicate whether the graph is symmetric with respect to the x-axis, the y axis, or the origin.

6 step solution

Q. 35

The graph of an equation is given.

(a). Find the intercepts.

(b). Indicate whether the graph is symmetric with respect to the x-axis, the y axis, or the origin.

6 step solution

Q. 36

The graph of an equation is given.

(a). Find the intercepts.

(b). Indicate whether the graph is symmetric with respect to the x-axis, the y axis, or the origin.

6 step solution

Q. 37

The graph of an equation is given.

(a). Find the intercepts.

(b). Indicate whether the graph is symmetric with respect to the x-axis, the y axis, or the origin.

6 step solution

Q. 38

The graph of an equation is given.

(a). Find the intercepts.

(b). Indicate whether the graph is symmetric with respect to the x-axis, the y axis, or the origin.

6 step solution

Q. 39

The graph of an equation is given.

(a). Find the intercepts.

(b). Indicate whether the graph is symmetric with respect to the x-axis, the y axis, or the origin.

6 step solution

Q. 40

The graph of an equation is given.

(a). Find the intercepts.

(b). Indicate whether the graph is symmetric with respect to the x-axis, the y axis, or the origin.

6 step solution

Q. 41

Draw a complete graph so that it has the type of symmetry indicated.

y-Axis

4 step solution

Q. 42

Draw a complete graph so that it has the type of symmetry indicated.

x-Axis

4 step solution

Q. 43

Draw a complete graph so that it has the type of symmetry indicated.

the origin

4 step solution

Q. 44

Draw a complete graph so that it has the type of symmetry indicated.

y-Axis

4 step solution

Q. 45

List the intercepts and test for symmetry.

$y^{2} = x + 4$

6 step solution

Q. 46

List the intercepts and test for symmetry -

$y^{2} = x + 9$

6 step solution

Q. 47

List the intercepts and test for symmetry -

$y = \sqrt[3]{x}$

6 step solution

Q. 48

List the intercepts and test for symmetry -

$y = \sqrt[5]{x}$

6 step solution

Q. 49

List the intercepts and test for symmetry -

$y = x^{4} - 8 x^{2} - 9$

6 step solution

Q. 50

List the intercepts and test for symmetry -

$y = x^{4} - 2 x^{2} - 8$

6 step solution

Q. 51

List the intercepts and test for symmetry -

$9 x^{2} + 4 y^{2} = 36$

6 step solution

Q. 52

List the intercepts and test for symmetry -

$4 x^{2} + y^{2} = 4$

6 step solution

Q. 53

In Problems 53, list the intercepts and test for symmetry.

$y = x^{3} - 27$

5 step solution

Q. 54

In Problems 54, list the intercepts and test for symmetry.

$y = x^{4} - 1$

5 step solution

Q. 55

In Problems 55, list the intercepts and test for symmetry.

$y = x^{2} - 3 x - 4$

5 step solution

Q. 56

In Problems 56, list the intercepts and test for symmetry.

$y = x^{2} + 4$

5 step solution

Q. 57

In Problems 57, list the intercepts and test for symmetry.

$y = \frac{3 x}{x^{2} + 9}$

5 step solution

Q. 58

In Problems 58, list the intercepts and test for symmetry.

$y = \frac{x^{2} - 4}{2 x}$

5 step solution

Q. 59

In Problems 59, list the intercepts and test for symmetry.

$y = \frac{- x^{3}}{x^{2} - 9}$

5 step solution

Q. 60

In Problems 60, list the intercepts and test for symmetry.

5 step solution

Q. 61

In Problems 61, draw a quick sketch of each equation.

$y = x^{3}$

5 step solution

Q. 62

In Problems 62, draw a quick sketch of each equation.

$x = y^{2}$

5 step solution

Q. 63

In Problems 63, draw a quick sketch of each equation.

$y = \sqrt{x}$

5 step solution

Q. 64

In Problems 64, draw a quick sketch of each equation.

$y = \frac{1}{x}$

5 step solution

Q .65

If $(3, b)$ is a point on the graph of $y = 4 x + 1$ , what is $b$ ?

3 step solution

Q. 65

If $(3, b)$ is a point on the graph of $y = 4 x + 1,$ what is b ?

3 step solution

Q. 66

If $(3, b)$ is a point on the graph of $2 x + 3 y = 2$ , what is $b$ ?

3 step solution

Q. 67

If $(a, 4)$ is a point on the graph of $y = x^{2} + 3 x$ , what is $a$ ?

3 step solution

Q. 68

If $(a, - 5)$ is a point on the graph of $y = x^{2} + 6 x$ , what is $a$ ?

3 step solution

Q. 78

If the graph of an equation is symmetric with respect to the $y$ -axis and 6 is an $y = x^{2} + 3 x$ -intercept of this graph, name another $x$ -intercept.

3 step solution

Q. 79

If the graph of an equation is symmetric with respect to the origin and $- 4$ is an $x$ -intercept of this graph, name another $x$ -intercept.

3 step solution

Q. 69

In Problems 69, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the $x$ -axis, the $y$ -axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.

$y = x^{2} - 5$

7 step solution

Q. 70

In Problems 70, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the $x$ -axis, the $y$ -axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.

$y = x^{2} - 8$

7 step solution

Q. 71

In Problems 71, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the $x$ -axis, the $y$ -axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.

$x - y^{2} = - 9$

7 step solution

Q. 72

In Problems 72, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the $x$ -axis, the $y$ -axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.

$x + y^{2} = 4$

7 step solution

Q. 73

In Problems 73, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to

assist in drawing the graph. Verify your results using a graphing utility.

$x^{2} + y^{2} = 9$

5 step solution

Q. 74

In Problems 74, (a) find the intercepts of each equation, (b) test each equation for symmetry with respect to the x-axis, the y-axis, and the origin, and (c) graph each equation by hand by plotting points. Be sure to label the intercepts on the graph and use any symmetry to assist in drawing the graph. Verify your results using a graphing utility.

$x^{2} + y^{2} = 16$

5 step solution

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