College Algebra (10th Edition)

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

Chapter 5 - Review Exercises: 6

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 $y=-f(x)$ involves a reflection about the x-axis of the parent function $f(x)$. The given function's parent function is $f(x) = x^4$. The given function can be written as $y=-f(x-1)$. Thus, the function involves: (i) a 1-unit shift to the right, and (ii) a reflection about the x-axis 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) reflect the graph in Step (2) above about the x-axis by changing the y-values to its opposite sign while keeping the values of $x$. (refer to the blue graph in the attached image in the answer part above)
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