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Chapter 2: Q. 7 (page 76)

True or False: The graph of a function y=fxalways crosses the y-axis.

Short Answer

Expert verified

The statement is false.

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

If there exists a function that does not have a y-intercept then it will not crosses the y-axis.

Let the function is

y=1x

The graph of this function never crosses the y-axis.

Therefore, the given statement "The graph of a function y=fxalways crosses the y-axis" is false.

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Most popular questions from this chapter

If f(x)=2x-4if-1鈮�x鈮�2x3-2if2<x鈮�3

Find: (a) f(0) (b) f(1) (c) f(2) (d)f(3)

The set of all images of the elements in the domain of a function is called the _________.

Exploration Graph y=x3. Then on the same screen graph y=(x-1)3+2. Could you have predicted the result?

In Problems 7鈥�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.

f(x)=x2+4
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