Answer:
A: f(x) is stretched away from the y-axis by a factor of 2
Step-by-step explanation:
Parent function:
[tex]f(x)=\cos(x)[/tex]
Given transformation:
[tex]g(x)=f\left(\dfrac{1}{2}x\right)=\cos \left(\dfrac{1}{2}x\right)[/tex]
Translation:
[tex]y=f(ax) \implies f(x) \: \textsf{stretched parallel to the x-axis by a factor of} \: \dfrac{1}{a}[/tex]
Therefore, f(x) is stretched parallel to the x-axis (horizontally) by a factor of 2:
[tex]a=\dfrac{1}{2} \implies \dfrac{1}{a}=\dfrac{1}{\frac{1}{2}}=2[/tex]
