Question

What is the equations for f(x)?

Answer 1

`f(x) = -8\cdot 4^x`

You reflect a function with respect to the
`x` axis by changing its sign.

In fact, if you consider the two alternatives

`x \mapsto f(x)` and
`x \mapsto -f(x)`

you can see that you're choosing opposite outputs for the same inputs.

In other words, one graph will be made of points like
`(x,f(x))`, the other of points like
`(x,-f(x))`

And the transformation

`(x,y) \to (x,-y)`

is exactly a reflection with respect to the
`x` axis.