Which statement best describes how the graph of g is a transformation of the graph of f?

g(x) = f(-x)

-The graph of g is vertical reflection across the x-axis of the graph of f
-The graph of g is a horizontal compression of the graph of f
-The graph of g is a horizontal reflection across the y-axis of the graph of f
-The graph of g is vertical stretch of the graph of f

it is symmetric about the y-axis, so ...

I'm guessing that means the answer is:

The graph of g is a horizontal reflection across the y-axis of the graph of f?

Say it said g(x) = -f(x)
would that just mean it is symmetric about the x-axis?

correct on both counts.

To determine how the graph of g is a transformation of the graph of f, we need to analyze the given equation g(x) = f(-x).

In this equation, f(-x) represents the value of the function f evaluated at -x. This means that for each input value x, we substitute -x into the function f to obtain the corresponding output.

Looking at the specific transformation in the equation, g(x) = f(-x), we can identify that there is a reflection happening across the y-axis. This is because substituting -x into f causes the x-values to switch signs, effectively reflecting the graph horizontally.

Therefore, the correct answer is:
-The graph of g is a horizontal reflection across the y-axis of the graph of f.