[tex] f(x) = -8\cdot 4^x [/tex]
You reflect a function with respect to the [tex] x [/tex] axis by changing its sign.
In fact, if you consider the two alternatives
[tex] x \mapsto f(x) [/tex] and [tex] x \mapsto -f(x) [/tex]
you can see that you're choosing opposite outputs for the same inputs.
In other words, one graph will be made of points like [tex] (x,f(x)) [/tex], the other of points like [tex] (x,-f(x)) [/tex]
And the transformation
[tex] (x,y) \to (x,-y) [/tex]
is exactly a reflection with respect to the [tex] x [/tex] axis.
