# Explain why the basic transformations of the parent function y=x^{5} will only generate functions that can be written in the form y=a(x - h)^{5} + k

Explain why the basic transformations of the parent function $y={x}^{5}$ will only generate functions that can be written in the form
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Sterp 1
When $y=f\left(x\right)$ is stretched vertically by a factor of $a,$ we get the graph for $y=af\left(x\right)$
When $y=f\left(x\right)$ is compressed vertically by a factor of$a$, we get the graph for $y=af\left(x\right)$
Note that we can also stretch the graph horizontall,
When $y=f\left(x\right)$ is stretched horizontally by a factor of m, we get the graph for $y=f\left(mx\right)$

Which is the same as a vertical shift by a factor $a={m}^{5}$
Therefore, by vertical and horizontal stretch of $y={x}^{5}$ we can obtain the polynomial $y=a{x}^{5}$
Step 2 When $y=f\left(x\right)$ is reflected across the x-axis, we get the graph for

When $y=f\left(x\right)$ is reflected across the y-axis, we get the graph for $y=f\left(-x\right)$

Note that sign of $a$ accounts for the reflection about x and y axes
Step 3
When