Question

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

Viewing rectangle $[-8,8]\mathrm{by}[6,6]$

(a) $y=\left|x\right|$

(b) $y=-\left|x\right|$

(c) $y=-3\left|x\right|$

(d) $y=-3|x-5|$

Short answer

(a) Graph of$y=\left|x\right|$

(b) Graph of$y=-\left|x\right|$

(c) Graph of$y=-3\left|x\right|$

(d) Graph of$y=-3|x-5|$

Step-by-step solution

Part a. Step 1. Given function.

Given function is$y=\left|x\right|$

Part a. Step 2. How to plot the graph.

To plot the graph, we use graphical calculator.

Part a. Step 3. Graph given.

The Graph of$y=\left|x\right|$

Part b. Step 1. Given function.

Given function is$y=-\left|x\right|$

Part b. Step 2. How to plot the graph.

To plot the graph, we use graphical calculator.

Part b. Step 3. Graph given.

The Graph of$y=-\left|x\right|$

Part c. Step 1. Given function.

Given function is$y=-3\left|x\right|$

Part c. Step 2. How to plot the graph.

To plot the graph, we use graphical calculator.

Part c. Step 3. Graph given.

The Graph of$y=-3\left|x\right|$

Part d. Step 1. Given function.

Given function is$y=-3|x-5|$

Part d. Step 2. How to plot the graph.

To plot the graph, we and graphical calculator.

Part d. Step 3. Graph given.

The Graph of$y=-3|x-5|$