Single Variable Calculus, Chapter 1, 1.3, Section 1.3, Problem 2

Explain how each function is derived from $y= f(x)$ by using an appropriate transformations as follows:

(a). $y=5f(x)$
The graph is stretched vertically by a factor of 5.
(b). $y=f(x-5)$
The graph is shifted 5 units to the right.
(c). $y=-f(x)$
The graph is reflected about the $x$-axis
(d). $y=-5f(x)$
The graph is stretched vertically by a factor of 5 and then reflected about the $x$ axis.
(e). $y=f(5x)$
The graph is compressed horizontally bya factor of 5.
(f). $y=5f(x) - 3$
The graph is stretched vertically by a factor of 5 then shifted 3 units downward.