SOLUTION: 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. Thank you!!

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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.
Thank you!!
Answer by funmath(2933) About Me  (Show Source):
You can put this solution on YOUR website!
Could someone please help me with this problem?
Graph y=2%5E%28x%29-3. 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%5E%28x%29-3
3=2%5Ex
ln%283%29=ln%282%5Ex%29
ln%283%29=xln%282%29
ln%283%29%2Fln%282%29=x
x=1.58492501 (0,1.58492501)
y-intercepts happen when x=0
y=2%5E0-3
y=1-3
y=-2 (-2,0)
graph%28300%2C200%2C-10%2C10%2C-10%2C10%2C2%5E%28x%29-3%29
Happy Calculating!!!