Question

The graph of a functionf is given. Sketch the graph of the following transformations off.

(a) $y=f\left(3x\right)$

(b) $y=f\left(\frac{1}{3}x\right)$

Short answer

Graph of the function are

(a) $y=f\left(3x\right)$

(b) $y=f\left(\frac{1}{3}x\right)$

Step-by-step solution

Part a. Step 1. Horizontal stretching and shrinking.

To graph $y=f\left(cx\right)$

If $c>1$, the graph of $y=f\left(x\right)$shrink horizontally by a factor of $\frac{1}{c}$.

If $0<c<1$, the graph of $y=f\left(x\right)$stretch horizontally by a factor of c.

Part a. Step 2. Graph of Solution

Given graph is

Part a. Step 3. Graph of Solution.

The graph of $y=f\left(3x\right)$ is

Part b. Step 1. Horizontal stretching and shrinking.

To graph $y=f\left(cx\right)$

If $c>1$, the graph of $y=f\left(x\right)$shrink horizontally by a factor of $\frac{1}{c}$.

If $0<c<1$, the graph of $y=f\left(x\right)$stretch horizontally by a factor of c.

Part b. Step 2. Graph of Solution.

Given graph is

Part b. Step 3. Graph of Solution.

The graph of$y=f\left(\frac{1}{3}x\right)$