Write an equation for the function g(x)

Question

Write an equation for the function g(x) whose graph is obtained from the graph of f(x)=x² by means of the following transformation:

 

a. compress the graph of f(x) horizontally by a factor of 1/2

 

b. Reflect the graph of f(x) across the x-axis and stretch vertically by a factor of 3.

Answer 1

Compress by factor of 2 = (2x)^2 = 4x^2

Then to reflect over x-axis multiply with -1 you get -4x^2

To stretch vertically by a factor of 3 multiply with 3 you get -12x^2