Chapter 1, Problem 9RE

Suppose that the graph of .f is given. Describe how the graphs of the following functions can be obtained from the graph of .f.

(a) y =.f(x) + 8

(b) y = f(x + 8)

(c) y = 1 + 2.f(x)

(d) y = f(x – 2) – 2

(c) y = –f(x)

(f) y = f^–1(x)

To determine

To explain: How the graph $y=f\left(x\right)+8$ is obtained from the graph of $y=f\left(x\right)$.

Answer to Problem 9RE

Solution:

The $y=f\left(x\right)$ graph shifted 8 units upward.

Explanation of Solution

It is given that the graph $y=f\left(x\right)+8$ is obtained from the graph of $y=f\left(x\right)$.

The graph of $y=f\left(x\right)+8$ can be obtained by shifting the graph $y=f\left(x\right)$ by 8 units upward.

To determine

To explain: How the graph $y=f\left(x+8\right)$ is obtained from the graph of $y=f\left(x\right)$.

Answer to Problem 9RE

Solution:

The $y=f\left(x\right)$ graph shifted 8 units to the left.

Explanation of Solution

It is given that the graph $y=f\left(x+8\right)$ is obtained from the graph of $y=f\left(x\right)$.

The graph of $y=f\left(x+8\right)$ can be obtained by shifting the graph $y=f\left(x\right)$ by 8 units to the left.

To determine

To explain: How the graph $y=1+2f\left(x\right)$ is obtained from the graph of $y=f\left(x\right)$.

Answer to Problem 9RE

Solution:

The $y=f\left(x\right)$ graph stretched 2 units vertically and then shifted 1 unit upward.

Explanation of Solution

It is given that the graph $y=1+2f\left(x\right)$ is obtained from the graph of $y=f\left(x\right)$.

The graph of $y=1+2f\left(x\right)$ can be obtained by stretching the graph $y=f\left(x\right)$ vertically by a factor of 2 and then shifting 1 unit upward.

To determine

To explain: How the graph $y=f\left(x-2\right)-2$ is obtained from the graph of $y=f\left(x\right)$.

Answer to Problem 9RE

Solution:

The $y=f\left(x\right)$ graph shifted 2 units to the right and then shifted 2 units downward.

Explanation of Solution

It is given that the graph $y=f\left(8x\right)$ is obtained from the graph of $y=f\left(x\right)$.

The graph of $y=f\left(x-2\right)-2$ can be obtained by shifting the graph $y=f\left(x\right)$ by 2 units to the right and then 2 units downward.

To determine

To write: How the graph $y=-f\left(x\right)$ is obtained from the graph of $y=f\left(x\right)$.

Answer to Problem 9RE

Solution:

The $y=f\left(x\right)$ graph reflected about the x-axis.

Explanation of Solution

It is given that the graph $y=-f\left(x\right)$ can be obtained from the graph of $y=f\left(x\right)$. The graph of $y=-f\left(x\right)$ can be obtained by reflecting the graph $y=f\left(x\right)$ about the x-axis.

To determine

To write: How the graph $y=f^{-1}\left(x\right)$ is obtained from the graph of $y=f\left(x\right)$.

Answer to Problem 9RE

Solution:

The $y=f\left(x\right)$ graph is reflected about the line y = x.

Explanation of Solution

It is given that the graph $y=f^{-1}\left(x\right)$ is obtained from the graph of $y=f\left(x\right)$.

The graph of $y=f^{-1}\left(x\right)$ can be obtained by reflecting the graph $y=f\left(x\right)$ about the line $y=x$.