We're choosing among
[tex]y = \pm 4^{\pm x}[/tex]
and we have to figure out which signs goes with which graph.
If they're both positive we have a pretty normal exponential,
[tex]y = 4^x[/tex]
That's going to be zero as x gets negative and exponentially explode toward positive infinity for positive x. Graph 3.
[tex]y = -4^x[/tex]
That's the same as the last one except it goes to negative infinity. It's the last one reflected in the x axis. Graph 4.
[tex]y = (\frac 1 4)^x[/tex]
When we have a fraction between 0 and 1 for the base as x gets bigger this goes to zero and as x gets more negative, this diverges toward positive infinity. It's our first graph reflected in the y axis, the same as [tex]y=4^{-x}[/tex]. That's our first graph reflected in the y axis. Graph 1.
[tex]y = (-\frac 1 4)^x[/tex]
That's the same as [tex]y=-4^{-x}[/tex]. As x gets more negative y diverges toward negative infinity. Graph 2.
