What is the equation of y=x^3 with the given transformations? Vertical compression by a factor of 1/7 ,horizontal shift 8 units to the left, reflection across the x axis

The transformed equation of is .

Given equation:-

Applying the given transformations, we have:

To have a vertical compression by a factor of , we need to multiply the function by . So, we have:

To have a horizontal shift by 8 units to the left, we need to add 8 to x. So, we have:

Lastly, to have a reflection over the x-axis, we need to multiply the function by −1. So, we have:

Therefore, the transformed equation is

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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

f(x) = x^3 -2x^2 -3x

x( x^2 -2x-3)

x( x^2 +x -3x -3)

x( x(x+1) -3(x+1))

x( x-3)( x+1)

so zeroes are 0, 3,-1

its (2) option