Can I please get help?

Question

The point (1,-18) is on the graph of y=f(x) (there is no actual graph it’s just in the question). Find the point on the graph of the given transformed function.

g(x)= -6f(2x)

g(x)= F(x-9)

g(x) = f(-x)

Answer 1

I got this:

g(x)= -6f(2x) -> (1/2,-104)

g(x)= F(x-9) -> (10,-18)

g(x) = f(-x) -> (-1,-18)

I will explain this for a last example and you do a rest. What is f(-x)? It is the same as f(-1 * x). I rewrote f(-x) this way, so you can see "x" more clearly, this will help going forward. Now, what do we know about our original function? We know that when x=1, f(1) = -18. So, let's try use x=1 because we know what our function value (-18) will be for x=1. g(1) = f(-1 * 1) = f(-1) = ? What now? We stack because we have no idea what value our original function is for f(-1). However this helped us to figured what our next step should be. We need to find such value for x that our argument will be 1!!! We need that 1 because this is all we know.

Let's do it:

-1 * X = 1

X = -1.

Great ! Now we can use this -1. g(-1) = f(-1 * -1) = f(1) = - 18. This is it. g(-1) = -18, so our point for this function is (-1,-18).