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Chapter 2: Q. 43 (page 69)

In Problems 39– 46, find the following for each function:

(a)f(0)(b)f(1)(c)f(-1)(d)f(-x)(e)-f(x)(f)f(x+1)(g)f(x)(h)f(x+h)

f(x)=x+4

Short Answer

Expert verified

The value of

f(0)=4f(1)=5f(-1)=5f(-x)=x+4-f(x)=-x-4f(x+1)=x+5f(x)=x+4f(x+h)=x+h+4

Step by step solution

01

Step 1. Given Information

We have to find the value for each function:

(a)f(0)(b)f(1)(c)f(-1)(d)f(-x)(e)-f(x)(f)f(x+1)(g)f(x)(h)f(x+h)

The given equation isf(x)=x+4

02

Part (a) Step 1. We find the value of  f(0)Putting x=0 in the given question.

f(0)=0+4f(0)=4

03

Part (b) Step 1. We find the value of  f(1)Putting x=1 in the given question.

f(1)=1+4f(1)=1+4f(1)=5

04

Part (c) Step 1. We find the value of f(-1)Putting x=-1 in the given question.

f(-1)=-1+4f(-1)=1+4f(-1)=5

05

Part (d) Step 1. We find the value of f(-x)Putting x=-x in the given question.

f(-x)=-x+4f(-x)=x+4

06

Part (e) Step 1. We find the value of -f(x)To find the value we multiply the given equation by -sign

-f(x)=-x+4-f(x)=-x-4

07

Part (f) Step 1. We find the value of f(x+1)Putting x=x+1 in the given question.

f(x+1)=x+1+4f(x+1)=x+1+4f(x+1)=x+5

08

Part (g) Step 1. We find the value of f(x)

The value off(x)=x+4

09

Part (h) Step 1. We find the value of f(x+h)Putting x=x+h in the given question.

f(x+h)=x+h+4f(x+h)=x+h+4

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Most popular questions from this chapter

In Problems 33– 44, determine algebraically whether each function is even, odd, or neither.

g(x)=x2+3x2-1

In Problems 7–18, match each graph to one of the following functions:

A.y=x2+2B.y=-x2+2C.y=x+2D.y=-x+2E.y=(x-2)2F.y=-(x+2)2G.y=x-2H.y=-x+2I.y=2x2J.y=-2x2K.y=2xL.y=-2x

Graph y=x. Then on the same screen graph y=2x, followed by y=4x, followed by

y=12x.What pattern do you observe? Can you predict the graph ofy=14x? ofy=5x

?

If fis a function defined by the equation y=f(x), then x is called the ____________ variable and y is the ____________ variable.

Graph the function using the techniques of shifting, compressing, stretching, and/or reflecting. Start with the graph of the basic function and show all stages. Be sure to show at least three key points. Find the domain and the range of each function. Verify your results using a graphing utility.

g(x)=x3+1
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