The transformed equation of [tex]y = x^{3}[/tex] is [tex]y = -\frac{1}{7} (x + 8)^{3}[/tex].
Given equation ; [tex]y = x^{3}[/tex]
Applying the given transformations, we have:
To have a vertical compression by a factor of [tex]\frac{1}{7}[/tex], we need to multiply the function by [tex]\frac{1}{7}[/tex]. So, we have:
[tex]y =[/tex] [tex]\frac{1}{7}[/tex] [tex]x^{3}[/tex]
To have a horizontal shift by 8 units to the left, we need to add 8 to x. So, we have:
[tex]y = \frac{1}{7} (x + 8)^{3}[/tex].
Lastly, to have a reflection over the x-axis, we need to multiply the function by −1. So, we have:
[tex]y = -\frac{1}{7} (x + 8)^{3}[/tex].
Therefore, the transformed equation is [tex]y = -\frac{1}{7} (x + 8)^{3}[/tex].
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