Precalculus (10th Edition)

Published by Pearson

Chapter 2 - Functions and Their Graphs - 2.5 Graphing Techniques: Transformations - 2.5 Assess Your Understanding - Page 104: 44

Answer

See graph Domain: $[-1,\infty)$ Range: $[0,\infty)$

Work Step by Step

We are given the function: $h(x)=\sqrt{x+1}$ We start with the basic function $a(x)=\sqrt x$. We horizontally shift $a(x)$ one unit to the left to get $h(x)=\sqrt{x+1}$. We use 3 points: $(-1,0),(0,1),(3,2)$ The domain of $h$ is: $D=[-1,\infty)$ The range of $h$ is: $R=[0,\infty)$

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