Question

The graph of y=5^x has ________.
asymptote at x=0
no asymptotes
an asymtote at y=0
an asymptote at y=x

Answer 1

at y = 0

Answer 2

Can you please show me how you figured that out?

Answer 3

as x -> +infinity, y-> +infinity
as x -> -infinity, y -> 1/(5^x) = 1/infinity = 0
y can never be less than 0, no matter what value of x

Answer 4

it might be better to express it as a limit.
\[\lim_{x \rightarrow -\infty}5^x=0\]

Answer 5

Thanks guys!