Can you help me identify any asymptotes that the function g(x)=-(5/3)^x might have?
hi
$\displaystyle \lim_{x\to +\infty }f(x) = -\infty $ $\displaystyle \Rightarrow$ $\displaystyle \lim_{x\to +\infty }\frac{f(x)}{x} = -\infty $
which means the y-axis is an asymptote.
and you also have :
$\displaystyle \lim_{x\to -\infty }f(x) = 0 \Rightarrow \lim_{x\to -\infty }\frac{f(x)}{x} = 0$
which means the x-axis is an asymptote.
Good thought Raoh, but this is not the case. Look at the graph skeeter has posted.
You can think of a vertical asymptote as any value of the function of x that x is "not allowed" to be. Is there any such value?
Limits at infinty tell us about y, not x. Think about what you said. By makink the statement $\displaystyle \lim_{x\to\infty}f(x)$, you're assuming that x can be ANY NUMBER!
P.S. You were correct about the horizotal asymptote.