Answer: Hello mate!
we have the function y = f(x) and we want to see how the next changes affect the graph of it:
a) y = 5f(x)
this is a "dilatation" in the y-axis, this means that the graph is 5 times higher than the original graph.
b) y = f(x − 4)
Now we have y = f(0) when x = 4, so here we have the whole graph translated to the right by 4 units
c) y = −2f(x)
This case is similar to the case in a, here we have dilatation of 2 units, but also the points where before the graph was positive, now is negative, and where the graph was negative, now is positive.
So we also have a reflection over the x-axis
d) y = f(3x)
Now, in the point x = 1, we have the value of y = f(3), this means that the value of y = f(1) is in between the x values of 0 and 1, then this is a contraction in the x-axis by 3 times.
e. y = 2f(x) − 5
Ok, here we have two things.
First, you can see another dilatation in the y-axis, but here we also have a subtraction of a constant, this means that the graph is dilated two times in the y-axis, and is translated by -5 units in the y-axis ( translated down by 5 units)