What are some examples of functions with asymptotes?

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Answer 1 · 2014-09-27T01:59:41

Example 1: $f (x) = \frac{x^{2}}{(x + 2) (x - 3)}$ $f(x)=x^2/{(x+2)(x-3)}$

Vertical Asymptotes: $x = - 2$ $x=-2$ and $x = 3$ $x=3$
Horizontal Asymptote: $y = 1$ $y=1$
Slant Asymptote: None

Example 2: $g (x) = e^{x}$ $g(x)=e^x$

Vertical Asymptote: None
Horizontal Asymptote: $y = 0$ $y=0$
Slant Asymptote: None

Example 3: $h (x) = x + \frac{1}{x}$ $h(x)=x+1/x$

Vertical Asymptote: $x = 0$ $x=0$
Horizontal Asymptote: None
Slant Asymptote: $y = x$ $y=x$

I hope that this was helpful.