College Algebra (6th Edition)

Published by Pearson
ISBN 10: 0-32178-228-3
ISBN 13: 978-0-32178-228-1

Chapter 2 - Functions and Graphs - Exercise Set 2.5 - Page 283: 68


please see image (graph of g(x) is red) .

Work Step by Step

$f(x)=\sqrt{x}$ Using, we graph f(x) (blue dashed graph) By hand, we would select some values for x and make a table with x ... f(x) as columns. Each pair gives a point on the graph of f(x). (In the screenshot, the table is to the left ) Plotting the points (x,f(x)) and joining them with a smooth curve, we have the graph of f(x). Using Table 2.4, Summary of Transformations, we see that $g(x)=\sqrt{x}+1=f(x)+1$ belongs to the group: "Vertical shifts $y=f(x)+c$ Raise the graph of $f$ by $c$ units. $c$ is added to $f(x)$." So, we add another column to our table, which will contain $f(x)+1.$ We plot the points ( x, f(x)+1 ), join them with a smooth curve, (red solid line on the screenshot), and we have the graph of g(x)
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