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Chapter 2: Q. 8 (page 76)

True or False: The y-intercept of the graph of the function y=fx, whose domain is all real numbers, is f0.

Short Answer

Expert verified

The statement is true.

Step by step solution

01

Step 1. Definition

f is the symbol that we use to denote the function. It is symbolic of the equation (rule) that we use to get from an x in the domain to f(x) in the range.

02

Step 2. Final answer

The y-intercept of the graph is obtained when x=0. So, the value of the function will be f0.

Therefore, the given statement "The y-intercept of the graph of the function y=fx, whose domain is all real numbers, is f0" is true.

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Most popular questions from this chapter

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 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)=12x

Suppose that the graph of a function fis known. Then the graph of y=f(-x) may be obtained by a reflection about the ________-axis of the graph of the function y=f(x).

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

If f(x)=x+1and g(x)=x3, then____________ =x3-(x+1).
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