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: 45

Answer

Refer to the blue graph below.
1511922777

Work Step by Step

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 $y=f(x)+c$ 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 $y=x^2$. The given function can be written $y=f(x-3)+5$ where $f(x)$ is the parent function. Thus, the graph of the given function involves (i) a horizontal shift of $3$ units to the right and (2) a vertical shift of $5$ units upward of the parent function $y=x^2$. Therefore, to graph the given function: (1) Graph the parent function $y=x^2$ . (Refer to the red graph in the attached image below) (2) Shift the graph of the parent function 3 units to the right. (Refer to the orange graph in the attached image below.) (3) Shift the graph in Step (2) 5 units upward. (Refer to the blue graph in the attached image in the answer part above)
Small 1511922777
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