Asymptotes

**HMV** · June 30th 2009, 10:53 AM

Can you help me identify any asymptotes that the function g(x)=-(5/3)^x might have?

**skeeter** · June 30th 2009, 10:57 AM

Originally Posted by HMV

Can you help me identify any asymptotes that the function g(x)=-(5/3)^x might have?

have you taken a look at the graph?

**Raoh** · June 30th 2009, 01:19 PM

hi

$\lim_{x\to +\infty }f(x) = -\infty$ $\Rightarrow$ $\lim_{x\to +\infty }\frac{f(x)}{x} = -\infty$
which means the y-axis is an asymptote.
and you also have :
$\lim_{x\to -\infty }f(x) = 0 \Rightarrow \lim_{x\to -\infty }\frac{f(x)}{x} = 0$
which means the x-axis is an asymptote.

**VonNemo19** · June 30th 2009, 01:25 PM

Originally Posted by Raoh

hi

$\lim_{x\to -\infty }f(x) = 0 \Rightarrow \lim_{x\to -\infty }\frac{f(x)}{x} = 0$
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 $\lim_{x\to\infty}f(x)$ , you're assuming that x can be ANY NUMBER!

P.S. You were correct about the horizotal asymptote.

**Raoh** · June 30th 2009, 02:09 PM

Awesome,thanks a lot,

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