College Algebra 7th Edition

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

Chapter 2, Functions - Section 2.6 - Transformations of Functions - 2.6 Exercises - Page 243: 48

Answer

Refer to the blue graph below.
1511924481

Work Step by Step

The given function can be written as: $y = -\sqrt{x+1}+2$ RECALL: (1) The function $y=f(x-h)$ involves a horizontal shift of $h$ units to the right of the parent function $f(x)$ when $h\gt0$. The function involves a horizontal shift of $|h|$ units to the left when $h \lt0$. (2) The function $y=-f(x)$ involves a reflection about the x-axis of the parent function $f(x)$. (3) The function $y=a\cdot f(x)$ involves a vertical stretch of the parent function $f(x)$ when $a\gt1$, and involves a vertical compression when $0 \lt a \lt 1$. (4) The function $y=f(x)+c$ involves a vertical shift of $c$ units upward of the parent function $f(x)$ when $c \gt 0$. The function will involve a vertical shift of $|c|$ units downward when $c \lt 0$. The parent function of the given function is $f(x)=\sqrt{x}$. The given function can be written $y=-f(x+1)+2$ where $f(x)$ is the parent function. Thus, the graph of the given function involves: (i) a horizontal shift of $1$ unit to the left, (ii) a reflection about the x-axis, (iii) a shift of $2$ units upward of the parent function $f(x)=\sqrt{x}$. Therefore, to graph the given function: (1) Graph the parent function $y=\sqrt{x}$ . (Refer to the red graph in the attached image below) (2) Shift the graph of the parent function 1 unit to the left. (Refer to the orange graph in the attached image below.) (3) Reflect the graph in Step (2) 3 about the x-axis. (Refer to the green graph in the attached image below) (4) Shift the graph in Step (3) 2 units upward. (Refer to the blue graph in the attached image in the answer part above.)
Small 1511924481
Update this answer!

You can help us out by revising, improving and updating this answer.

Update this answer

After you claim an answer you’ll have 24 hours to send in a draft. An editor will review the submission and either publish your submission or provide feedback.