Chapter 1.3, Problem 2E

(a)

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 2E

The 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 $y=f\left(x\right)$.

Since 8 is added to $f\left(x\right)$, the graph of $y=f\left(x\right)+8$ is shifted 8 units upward.

(b)

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 2E

The 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 $y=f\left(x\right)$.

Since 8 is added to $x$, the graph $y=f\left(x+8\right)$ is shifted 8 units to the left.

(c)

To determine

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

Answer to Problem 2E

The graph stretched 8 units vertically.

Explanation of Solution

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

Since 8 is multiplied to $f\left(x\right)$, the graph $y=8f\left(x\right)$ is stretched 8 units vertically.

(d)

To determine

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

Answer to Problem 2E

The graph shrunk 8 units horizontally.

Explanation of Solution

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

Since 8 is multiplied to x, the graph $y=f\left(8x\right)$ is shrunk 8 units horizontally.

(e)

To determine

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

Answer to Problem 2E

The graph reflects the x-axis and shifted 1 unit downward.

Explanation of Solution

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

Since it is $-f\left(x\right)$ the graph is an odd function, it reflects about the x-axis.

Also, the graph $y=-f\left(x\right)-1$ is shifted 1 unit downward.

(f)

To determine

To write: How the graph $y=8f\left(\frac{1}{8}x\right)$ is obtained from the graph of $y=f\left(x\right)$.

Answer to Problem 2E

The graph is stretched horizontally and vertically by a factor of 8.

Explanation of Solution

It is given that the graph $y=8f\left(\frac{1}{8}x\right)$ is obtained from the graph of $y=f\left(x\right)$.Since 8 is multiplied to $f\left(x\right)$ and 8 is divided from $x$, the graph is stretched horizontally and vertically by a factor of 8.