Question

What happens when the function f(x)=cos(x) is transformed by the rule g(x)=f(1/2x)?

A: f(x) is stretched away from the y-axis by a factor of 2.
B: f(x) is compressed toward the y-axis by a factor of 1/2.
C: f(x) is compressed toward the x-axis by a factor of 1/2.

Answer 1

A: f(x) is stretched away from the y-axis by a factor of 2

Explanation:

Parent function:

`f(x)=\cos(x)`

Given transformation:

`g(x)=f\left((1)/(2)x\right)=\cos \left((1)/(2)x\right)`

Translation:

`y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis by a factor of} \: (1)/(a)`

Therefore, f(x) is stretched parallel to the x-axis (horizontally) by a factor of 2:

`a=(1)/(2) \implies (1)/(a)=(1)/((1)/(2))=2`