Answer:
I guess that we want to find the function g(x) for the 4 cases.
first, f(x) = -9*x + 1.
a) The graph of g is a reflection in the y-axis of the graph of f.
First remember: if we have the point (x,y) and we reflect it over the y-axis, we get (-x,y)
then g(x) = f(-x) = -9*-x + 1 = 9*x + 1.
b) The graph of g is a reflection in the x-axis of the graph of f.
if we have a point (x, y) and we reflect it over the x-axis, the point transforms into (x, -y)
then we have: g(x) = -f(x) = 9*x - 1
c) The graph of g is a horizontal translation 16 units right of the graph of f.
When we want to have a translation in the x-axis, we must change x by x - A.
If A is positive, this transformation moves the graph by A units to the right, in this case, A = 16.
g(x) = f(x - 16) = -9*(x - 16) + 1
d) The graph of g is a vertical translation 16 units down of the graph of f.
For vertical translations, if we want to move the graph by A units down (A positive) we should do y = f(x) - A
In this case, A = 16.
then: g(x) = f(x) - 16 = -9*x + 1 - 16 = -9*x - 15.
