Find the table of change and sketch the function  h(x)=x sqrt 4-x^2

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section: Chapter Questions
Problem 71RE
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Question

Find the table of change and sketch the function 

h(x)=x sqrt 4-x^2

 

Expert Solution
Step 1

Given function is h(x)=x4-x2

Let us find the domain of the given function                                           

Since we have square root term, we get

4-x20

Squaring on both sides we get,

4-x20(2-x)(2+x)0x-2     x2

The domain of the given function is -2x2

 

Step 2

Choose x values to evaluate h(x) to form a coordinates

At x = -2 , h(-2)=-24-(-2)2=-24-4=0

At x = 0 , h(0)=04-02=0

At x= 2, h(2)=24-22=24-4=0

The graph passes at y = 0 three times

For x approaches -2 , h(x) will be negative, for x approaches 2 , h(x) will be positive

 

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