Chapter 1.1, Problem 33E

### Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248

Chapter
Section

### Applied Calculus

7th Edition
Waner + 1 other
ISBN: 9781337291248
Textbook Problem

# In Exercises 31-36, sketch the graph of the given/unction, evaluate the given expressions, and then use technology to duplicate the graphs. Give the technology formula. [HINT: See Example 2.) f ( x ) = { x 2 if     − 2 < x ≤ 0 1 / x if     0 ≤ x ≤ 4 a. f ( − 1 ) b. f ( 0 ) c. f ( 1 )

To determine

To calculate: The values at a. f(1),bf(0) and. cf(1) for the function

f(x)={x2    2<x01x        0<x4} and also plot its graph and use technology to duplicate the graph,

Explanation

Given Information:

The provided function is,

f(x)={x2Â Â Â Â âˆ’2<xâ‰¤01xÂ Â Â Â Â Â Â Â 0<xâ‰¤4}

The functions are,

a.Â f(âˆ’1)

b.Â f(0)

c.Â f(1)

Calculation:

(a)

Consider the provided function,

f(x)={x2Â Â Â Â âˆ’2<xâ‰¤01xÂ Â Â Â Â Â Â Â 0<xâ‰¤4}

For x=âˆ’1 function is given as;

f(x)=x2

Substitute âˆ’1 for x in function, f(x)=x2.

f(x)=x2

Therefore, the value of f(âˆ’1) is âˆ’1.

(b)

Consider the provided function,

f(x)={x2Â Â Â Â âˆ’2<xâ‰¤01xÂ Â Â Â Â Â Â Â 0<xâ‰¤4}

For x=0 function is given as;

f(x)=x2

Substitute 0 for x in function, f(x)=x2.

f(0)=(0)2=0

Therefore, the value of f(0) is 0.

(c)

Consider the provided function,

f(x)={x2Â Â Â Â âˆ’2<xâ‰¤01xÂ Â Â Â Â Â Â Â 0<xâ‰¤4}

For x=1 function is given as;

f(x)=1x

Substitute 1 for x in function, f(x)=1x.

f(1)=11=1

Therefore, the value of f(1) is âˆ’1

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