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Chapter 5: Q 19. (page 268)

The graph of a function f is given. Use the horizontal-line test to determine whether f is one-to-one.

Short Answer

Expert verified

Yes, the given function is one-to-one.

Step by step solution

01

Step 1. Definition

A function is said to be one-to-one if any two different inputs in the domain correspond to two different outputs in the range.

The horizontal line test checks if a function is one-to-one. A one-to-one function has only one x-value for each y-value. If a horizontal line passes through a graph more than once, the function can't be one-to-one.

02

Step 2. Explanation  

Use horizontal line test

The given function is one-to-one because every horizontal line intersects the graph exactly one.

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Most popular questions from this chapter

The function f(x)=|x|is not one-to-one. Find a suitable restriction on the domain of f so that the new function that results is one-to-one. Then find the inverse of f.

A function y=f(x)is decreasing on the interval(0,5).What conclusions can you draw about the graph ofy=f-1(x)?

the function f is one-to-one. Find its inverse and check your answer.

f(x)=x2-42x2x>0

Iffx=ax, show thatfx+h-fxh=ax.ah-1hh鈮�0.

Answers are given at the end of these exercises. If you get a wrong answer, read the pages listed in red.

Solve:

x2+3x=4x
See all solutions

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