Chapter 3.2, Problem 42E

(a)

To determine

To select:A parent or a modification of a parent graph that the given specification..

Answer to Problem 42E

The parent or a modification of a parent graph that the given specification is listed below.

Explanation of Solution

1. Positive at its leftmost point and positive at its rightmost points.

The function for the above statement is,

  $y={\left(x-1\right)}^2$

2. Negative at its leftmost points and positive at its rightmost point.

The function for the above statement is,

  $y={\left(x+2\right)}^3$

3. Negative at its leftmost points and negative at its rightmost point.

The function for the above statement is,

  $y=-{\left(x+4\right)}^2$

4. Positive at its leftmost points and negative at its rightmost point.

The function for the above statement is,

  $y=-x^3$

(b)

To determine

To sketch: The related graph for each parent graph.

Answer to Problem 42E

The related graph for each parent graph is shown below.

Explanation of Solution

The graph for ${\left(x-3\right)}^2-5$ is shown below.

  

Figure (1)

The graph for ${\left(x-3\right)}^3-5$ is shown below.

  

Figure (2)

The graph for $-{\left(x-3\right)}^2-5$ is shown below.

  

Figure (3)

The graph for $-{\left(x-3\right)}^3-5$ is shown below.

  

Figure (4)

Therefore, the related graph are shown in Figure (1), (2), (3) and (4).

(c)

To determine

To write: The equation for each related graph for each parent graph.

Answer to Problem 42E

The equation for each related graph is stated below.

Explanation of Solution

The equation for graph shown in Figure (1) is,

  $y={\left(x-3\right)}^2-5$

The equation for graph shown in Figure (2) is,

  $y={\left(x-3\right)}^3-5$

The equation for graph shown in Figure (3) is,

  $y=-{\left(x-3\right)}^2-5$

The equation for graph shown in Figure (4) is,

  $y=-{\left(x-3\right)}^3-5$