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Chapter 3: Q. 383 (page 345)

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

Short Answer

Expert verified
  1. f(0)=0
  2. f蟺2=-1
  3. f-3蟺2=-1
  4. f(x)=0at x=-2蟺,-蟺,0,蟺,2蟺
  5. x-intercepts are (-2蟺,0),-蟺,0,0,0,蟺,0,2蟺,0
  6. y-intercept is (0,0)
  7. The domain of the function is -2蟺,2蟺
  8. The range of the function is-1,1

Step by step solution

01

Step 1. 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, the function crosses the y-axis at 0. So, f(0)=0

03

Part (b)  Step 1. To find fπ2 

Look at the graph of the function

In the graph we can see that When x=蟺2then y-value of the function is -1 So, f蟺2=-1


04

Part (c)  Step 1. To find f-3π2

Look at the graph of the function

In the graph we can see that When x=-3蟺2then yvalue of the function is -1 So,

05

Part(d) Step 1. To find value of x for which f(x)=0

Look at the graph

We observe that graph of the function has yvalue 0 at points

(-2蟺,0),(-蟺,0),(0,0),(蟺,0),(2蟺,0)

So the values of x=-2蟺,-蟺,0,蟺,2蟺for whichf(x)=0

06

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

The x-intercepts occur when y=0

So the x-intercepts occur when f(x)=0

The x-intercepts are(-2蟺,0),(-蟺,0),(0,0),(蟺,0),(2蟺,0)


07

Part (f) Step 1. To find y-intercepts

The y-intercepts occur whenx=0

So y-intercept is(0,0)

08

Part (g) Step 1. To find domain

This function has a definite value when xis from -2蟺to 2蟺 Therefore, the domain in interval notation is -2蟺,2蟺

09

Part (h). Step 1. To find range

This function values, or y-values go from -1 to 1 Therefore, the range, in interval notation, is-1,1

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