A function $f(x)$ is defined by the set of points: $$\{(-4,-5),(1,-1),(5,3)\}$$ If $g(x)=\frac{1}{2}f(x)$, which of the following represents the transformed set of points on the graph of $g$?

True or False: A vertical dilation $y=af(x)$ where $a>0$ always preserves the $x$-coordinates of the local maximum and minimum points of the original function $f(x)$.

Given the function $f(x)$, if $g(x)=f(bx)$ and the graph of $g$ is known to be a horizontal stretch of the graph of $f$, which of the following must be true about the constant $b$?

A function $f$ has a local maximum at $(2,5)$. What are the coordinates of the local maximum for the function h(x) = f\left(\frac{1}{4}x ight)

If the function $h$ is defined by $h(x)=f(0.4x)$, by what scale factor is the graph of $f$ dilated parallel to the $x$-axis to obtain the graph of $h$?