Question 59931
Could someone please help me with this problem?

Graph {{{y=2^(x)-3}}}. Label all x-intercepts, all y-intercepts, horizontal asymptotes, and vertical asymptotes.

There are no vertical asymptotes for exponential functions.
The horizontal asymptote happens normally at 0, because there is know power that will make anything =0.  Because of the -3, there is a horizontal asymptote at y=-3.
x-intercepts happen when y=0
{{{0=2^(x)-3}}}
{{{3=2^x}}}
{{{ln(3)=ln(2^x)}}}
{{{ln(3)=xln(2)}}}
{{{ln(3)/ln(2)=x}}}
{{{x=1.58492501}}}  (0,1.58492501)
y-intercepts happen when x=0
{{{y=2^0-3}}}
{{{y=1-3}}}
{{{y=-2}}}  (-2,0)
{{{graph(300,200,-10,10,-10,10,2^(x)-3)}}}
Happy Calculating!!!