College Algebra (10th Edition)

Published by Pearson
ISBN 10: 0321979478
ISBN 13: 978-0-32197-947-6

Chapter 5 - Review Exercises: 7

Answer

Refer to the blue graph below.
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Work Step by Step

RECALL: (1) The function $y=f(x-h)$ involves either a horizontal shift of $h$ units to the right of the parent function $f(x)$ if $h \gt0$, or a horizontal shift of $|h|$ units to the left when $h\lt0$. (2) The function $y=f(x)+k$ involves either a vertical shift of $k$ units upward of the parent function $f(x)$ when $k\gt0$, or a vertical shift of $|k|$ units downward when $k\lt0$. The given function's parent function is $f(x) = x^4$. The given function can be written as $y=f(x-1)+2$. Thus, the function involves: (i) a 1-unit shift to the right, and (ii) a 2-unit shift upward of the parent function $f(x)$ To graph the given function, perform the following steps: (1) Graph the parent function $f(x) = x^4$. (refer to the red graph below). (2) Shift the graph of the parent function 1 unit to the right. (refer to the green graph below) (3) shift the graph in Step (2) above 2 units upward by adding 2 to each of the y-values while keeping the values of $x$. (refer to the blue graph in the attached image in the answer part above)
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