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 243: 126


The possible equation for the given graph is $y=\sqrt{x-2}+1$.

Work Step by Step

The above given graph looks similar to the graph of the function $y=\sqrt{x}$, but the graph of $y=\sqrt{x}$ passes through the origin. So this graph should be called the shifted graph. The graph is right-shifted by unit $c$. Therefore, the variable $x$ is replaced by the factor $x-c$. So, the equation is: $\begin{align} & y=\sqrt{x} \\ & =\sqrt{x-c} \end{align}$ It can be clearly observed from the graph, that the value of $c$ is 2. So, $\begin{align} & y=\sqrt{x-c} \\ & =\sqrt{x-2} \end{align}$ Further the graph is shifted upwards vertically on the $y$ axis with unit 1. Then, $\begin{align} & y=\sqrt{x-2} \\ & =\sqrt{x-2}+1 \end{align}$ Hence, the graph of the function is in the form of $y=\sqrt{x-c}+a$. Where $c=2,a=1$. Hence, the possible function is $y=\sqrt{x-2}+1$.
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