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Chapter 3: Q. 386 (page 346)

In the following exercises, use the graph of the function to find the indicated value

Short Answer

Expert verified
  1. f(0)=4
  2. f(x)=0, for x=-4,4
  3. x-intercept is (-4,0),(4,0)
  4. y-intercept is (0,4)
  5. Domain of the function is -4,4
  6. Range of the function is 0,4

Step by step solution

01

. Given information

Graph of the function

02

Part (a) Step 1. To find f(0)

Look at the graph of the function

In the graph we can see that When x=0,then function crosses the y-axis at 4. So, f(0)=4

03

Part (b) Step 1.  To find value of  xfor which f(x)=0 

.Look at the graph

The graph of the function crosses x-axis atx=-4,4

Sof(x)=0 atx=-4,4

04

Part (c) Step 1. To find  x-intercepts  

As we know that x-intercept occurs when f(x)=0ory=0

and here f(x)=0atx=-4,4

So x- intercepts are-4,0,4,0

05

Part (d) Step 1. To find  y-intercept

The y-intercepts occur when x=0

here value off(0)=4

So y-intercept is(0,4)

06

Part (e) Step 1. To find domain of the function    

This function has a definite value when xis from -4 to 4 Therefore, the domain in interval notation is -4,4

07

Part (f) Step 1. To find range of the function   

This function values, or y-values go from 0 to 4 Therefore, the range, in interval notation, is 0,4

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