What is the range of #g(x)=6^x-3#?

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Answer 1 · 2018-04-17T18:31:00

#[-3,oo)#

#g(x)=6^x-3#

as #x->oo \ \ \ \ \ \ \ \ \ #, #6^x-3->oo#

Notice when #x<0 \ \ \ \ \ \# #6^x-3->1/6^x-3#

as #x->-oo \ \ \ \ \ \ \ \#, #1/6^x-3->0-3=-3#

So the range of the function is:

#[-3,oo)#

The graph of #f(x)=6^x-3# confirms this:

enter image source here