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.