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Chapter 2: Q. 6 (page 76)

True or False: A function can have more than one y-intercept.

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

A set of points in the xy-plane is the graph of a function if and only if every vertical line intersects the graph in at most one point.

Therefore, the given statement "A function can have more than one y-intercept" is false.

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Most popular questions from this chapter

A semicircle of radius r is inscribed in a rectangle so that the diameter of the semicircle is the length of the rectangle. See the figure.

(a) Express the area A of the rectangle as a function of the radius r of the semicircle.

(b) Express the perimeter p of the rectangle as a function of r.

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)=x+23-3

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

?

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)=2x3

match each graph to its function.

A. Constant function

B. Identity function

C. Square function

D. Cube function

E. Square root function

F. Reciprocal function

G. Absolute value function

H. Cube root function
See all solutions

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