Chapter 2.5, Problem 35AYU

In Problem 27-30, find the function that is finally graphed after each of the following transformations is applied to the graph of $y\text{ = }\sqrt{x}$ in the order stated.

Suppose that the $x\text{-intercepts}$ of the graph of $y\text{ = }f\left(x\right)$ are $-5$ and $3$.

(a) What are the $x\text{-intercepts}$ of the graph of $y\text{ = }f\left(x\text{ + 2}\right)$?

(b) What are the $x\text{-intercepts}$ of the graph of $y\text{ = }f\left(x\text{ - 2}\right)$?

(c) What are the $x\text{-intercepts}$ of the graph of $y\text{ = 4}f\left(x\right)$?

(d) What are the $x\text{-intercepts}$ of the graph of $y\text{ = }f\left(-x\right)$?

To determine

To find: Suppose that the $x\text{-intercepts}$ of the graph of $y=f\left(x\right)$ are $-5$ and 3, to find the following:

a. The $x\text{-intercepts}$ of the graph of $y=f\left(x+2\right)$.

Answer to Problem 35AYU

a. The $x\text{-intercepts}$ of the graph of $y=f\left(x+2\right)$ is $-7\text{ and }1$.

Explanation of Solution

Given:

The $x\text{-intercepts}$ of the graph of $y=f\left(x\right)$ are $-5$ and 3.

a. The $x\text{-intercepts}$ of the graph of $y=f\left(x+2\right)$.

Horizontally shift left 2 units.

We get $-7$ and 1.

To determine

To find: Suppose that the $x\text{-intercepts}$ of the graph of $y=f\left(x\right)$ are $-5$ and 3, to find the following:

b. The $x\text{-intercepts}$ of the graph of $y=f\left(x-2\right)$.

Answer to Problem 35AYU

b. The $x\text{-intercepts}$ of the graph of $y=f\left(x-2\right)$ is $-3\text{ and }5$.

Explanation of Solution

Given:

The $x\text{-intercepts}$ of the graph of $y=f\left(x\right)$ are $-5$ and 3.

b. The $x\text{-intercepts}$ of the graph of $y=f\left(x-2\right)$.

Horizontally shift right 2 units.

We get $-3$ and 5.

To determine

To find: Suppose that the $x\text{-intercepts}$ of the graph of $y=f\left(x\right)$ are $-5$ and 3, to find the following:

c. The $x\text{-intercepts}$ of the graph of $y= 4f\left(x\right)$.

Answer to Problem 35AYU

c. The $x\text{-intercepts}$ of the graph of $y= 4f\left(x\right)$ is $-5\text{ and }3$.

Explanation of Solution

Given:

The $x\text{-intercepts}$ of the graph of $y=f\left(x\right)$ are $-5$ and 3.

c. The $x\text{-intercepts}$ of the graph of $y= 4f\left(x\right)$.

Vertically stretched by a factor of 4.

We get $-5$ and 3.

To determine

To find: Suppose that the $x\text{-intercepts}$ of the graph of $y=f\left(x\right)$ are $-5$ and 3, to find the following:

d. The $x\text{-intercepts}$ of the graph of $y=f\left(-x\right)$.

Answer to Problem 35AYU

d. The $x\text{-intercepts}$ of the graph of $y=f\left(-x\right)$ is $-3\text{ and }5$.

Explanation of Solution

Given:

The $x\text{-intercepts}$ of the graph of $y=f\left(x\right)$ are $-5$ and 3.

d. The $x\text{-intercepts}$ of the graph of $y=f\left(-x\right)$.

Reflection about the $y\text{-axis}$.

We get $-3$ and 5.