Question

When examining the formula of a function that is the result of multiple transformations, how can you tell a reflection with respect to the x-axis from a reflection with respect to the y-axis

Answer 1

For a function f(x), a reflection across the y-axis is written as:

g(x) = f(-x)

While a reflection across the x-axis is written as:

g(x) = -f(x)

So, if the negative sign is outside the transformation, like in:

g(x) = -f(x + 2) - 8

We can conclude that this is a reflection over the x-axis.

While if the "x" inside the function has a negative sign, like in:

g(x) = 5*f(-x + 4) - 3

The reflection is over the y-axis.