Respuesta :
Answer:
y = (1/7)(x + 8)³
Step-by-step explanation:
We are given the function; y = x³
There is a vertical compression by a factor of 1/7 which means that we now have the function as;
y = (1/7)x³
We are told that it shifts by 8 units to the left. This means we will have;
f(x + 8)
This gives;
y = (1/7)(x + 8)³
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=\frac{1}{7} 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]
For more information:
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