Let the graph of g be a vertical shrink by a factor of 12, followed by a translation 3 units to the left of the graph of f(x)=2x3−4x. Write a rule for g.

Question

Hello, please help me. Also explain why.

Answer 1

If you are shrinking it vertically then you are making the function wider which means you need to multiply the whole function by a factor less than 1.

When you want to move the function to the left, then you need to add to x the specified value at each instance.

For this prproblem, let's first shift left, then shrink vertically.

You have:

Y=2x³-4x.

To shift 3 units to the left, then add 3 at each instance of X:

Y=2(x+3)³-4(x+3)

To shrink the function vertically by a factor of 12, then you want to multiply the function by (1/12) so you get:

Y= (2/12)(x+3)³-(4/12)(x+3)

Y=(1/6)(x+3)³-(1/3)(x+3)