- #1
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Homework Statement
I am unsure how to find the asymptotes and thus, graph the function of -
[tex]f(x)=\frac{x+4}{x^{2}-4}[/tex]
Homework Equations
Such functions that have the same degree polynomial in both the numerator and denominator can be simplified to change the numerator from a variable in x, to a constant which helps to find the asymptotes.
e.g.
[tex]y=\frac{x-2}{x+5}[/tex]
[tex]y=\frac{(x+5)-7}{x+5}[/tex]
[tex]y=1-\frac{7}{x+5}[/tex]
Therefore it can be seen that there is an asymptote at y=1 - since the fraction [tex]\neq[/tex] 0 - and another at x=-5 since the denominator of the fraction [tex]\neq[/tex] 0
The Attempt at a Solution
The first asymptote is obvious, x=[tex]\pm[/tex]2 since the denominator [tex]\neq[/tex] 0
Then I split the function into a similar form as shown with the e.g.
[tex]f(x)=\frac{(x+2)+2}{(x+2)(x-2)}[/tex]
[tex]f(x)=\frac{1}{x-2}+\frac{2}{(x+2)(x-2)}[/tex]
but from here I'm unsure how to find the y asymptotes. Could someone please show me the solution, or point me in the right direction?