Precalculus (6th Edition) Blitzer

Published by Pearson
ISBN 10: 0-13446-914-3
ISBN 13: 978-0-13446-914-0

Chapter 1 - Section 1.6 - Transformations of Functions - Exercise Set - Page 241: 4

Answer

See the graph below:

Work Step by Step

Consider the graph of $f\left( x \right)$ as shown above. The function $g\left( x \right)$ is given by the equation as follows: $g\left( x \right)=f\left( x-1 \right)$ The given function is in the form of $g\left( x \right)=f\left( x+c \right)$. In the above case, the graph shifts horizontally. If the number c is positive, then the graph will shift to the left by c units, and if the number c is negative, then the graph will shift to the right by c units. According to the function of $g\left( x \right)$ , the function $f\left( x \right)$ is shifted by 1 unit in the right direction. $g\left( x \right)=f\left( x-1 \right)$ is the function for $g\left( x \right)$. This means that all the x terms are replaced by $x-1$ in the function. The values of the function earlier obtained at x will now be obtained at $x+1$. We see that $-1$ is negative, so the graph will shift 1 unit right.
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