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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

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

F(x)=2xx

True or False

To obtain the graph of f(x)=x3+5,shift the graph of y=x3vertically up 5units.

A wire of length xis bent into the shape of a circle.

Part (a): Express the circumference Cof the circle as a function of x.

Part (b): Express the areaAof the circle as a function ofx.

Concepts and Vocabulary

A function f is ___________ on an open interval I if, for any choice of x1 and x2 in I, withx1<x2wehavef(x1)<f(x2)

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.

h(x)=12x
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