Question

What transformations change the graph of f(x) to the graph of g(x)?

f(x) = -5x^2, g(x) = -20x^2-8

Please provide explanation​

Answer 1

i) Transformation is first horizontally shrinking by a scale factor of 2 and then

ii) vertically shifting down by 8 units.

Explanation:

given that original graph is
`f(x) = -5x^2`

It is first shrunk by a scale factor of 2 horizontally.

i.e. x = 2X

Hence we got f(x) transformed = -5(2x)^2 = -20x^2

Next transformation is vertically down by 8 units.

Now new function is f2(x) = -20x^2-8

This is our g(x) = -20x^2-8

Thus we have a series of two transformations as

i) Horizontally shrinking by a scale factor of 2

ii) followed by vertical shifting down by 8 units.