## College Algebra (10th Edition)

Published by Pearson

# Chapter 3 - Section 3.5 - Graphing Techniques: Transformations - 3.5 Assess Your Underdstanding: 26

#### Answer

$y=\frac{1}{4}(x)^3$

#### Work Step by Step

RECALL: (i) $y=-f(x)$ involves a reflection about the x-axis of the parent function $y=f(x)$. (ii) $y=f(-x)$ involves a reflection about the y-axis of the parent function $y=f(x)$. (iii) $y=af(x)$ involves either a vertical compression by a factor of $a$ of the parent function $f(x)$ when $a\gt 1$ or a vertical stretch when $0 \lt a \lt 1$. (iv) $y=f(x-h)$ involves a horizontal shift of either $h$ units to the right of the parent function $f(x)$ when $h \gt 0$ or $|h|$ units to the left when $h \lt0$. (v) $y=f(x) + k$ involves either a vertical shift of $k$ units upward of the parent function when $k\gt 0$ or $|k|$ units downward when $k \lt0$. The graph involves a horizontal stretch by a factor of $4$ of the parent function. Using the equation in (iv) above gives: $a=\dfrac{1}{4}$ Thus, the function is $y=f(\frac{1}{4}x) \\y=\frac{1}{4}(x)^3$

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