How do you graph #y=-3*2^(x+2)#?

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Answer 1 · 2017-07-20T09:09:36

#y# has the standard graph of #2^x# scaled by #-12#

#y=-3*2^(x+2)#

Since #2^(x+2)>0 forall x in RR -> y<0 forall x in RR#

In other words, #y# is always negative.

Now let's consider some other criteria of #y#

#lim_(x->-oo) y =0#

#lim_(x-> +oo) y = -oo#

#y(0) = -3* 2^2 = -12#

#y = -3xx2^2 * 2^x = -12*2^x#

#y# has the standard graph of #2^x# scaled by #-12#

The graph of #y# is shown below.

graph{-3*2^(x+2) [-36.3, 36.8, -29.95, 6.53]}