College Algebra 7th Edition

Published by Brooks Cole
ISBN 10: 1305115546
ISBN 13: 978-1-30511-554-5

Chapter 2, Functions - Chapter 2 Test: 12

Answer

(a) yes, one-to-one (b) not one-to-one

Work Step by Step

(a) The function $f(x)=x^3+1$ is one-to-one. It passes the horizontal line test (it is a shifted cubic function, which is odd). Since the equation only contains a cube and addition, every unique $x$ value will have a unique $y$ value, ensuring that the function is one-to-one. (b) The function $g(x)=|x+1|$ is not one-to-one because we can find two $x$ values that will produce the same $y$ value. For example: $g(0)=|0+1|=|1|=1$ $g(-2)=|-2+1|=|-1|=1$ Thus the function is not one-to-one.
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