Question

The function g(x) = 8(4x) is reflected across the x-axis to create f(x). What is the equation for f(x)? f(x) =_____ (4)x

Answer 1

`f (x) = -8(4x)`

Explanation:

The transformation that reflects the function
`g(x)` on the axis is:

`y = -g (x)`.

Therefore if we have the function

`g (x) = 8 (4x)` and we call
`f (x)` to the transformation that relieves g (x) on the x axis then:

`f (x) = -g (x)\\\\f (x) = -8(4x)`

Finally the equation for f(x) es:
`f (x) = -8(4x)`

Answer 2

f(x) = -8(4)x

Explanation:

The reflection of the point (x,y) across the x-axis is the point (x,-y).

Having said this, to reflect the function y=g(x) = 8(4x) over the x-axis, we just need to evaluate the equation in the point: (x,-y).

y = 8(4x) ⇒ -y = 8(4x) ⇒ y = -8(4x)

Then f(x) = -8(4x)

Attached you will find the graph of g(x) (blue) and f(x) (red),