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**Unformatted text preview: **nd the left. p( x)
f ( x) =
If
q( x) is a rational function in lowest terms,
then the line x = a is vertical asymptote to the graph of
f(x) if and only if q(a) = 0 . Ex 2. Find the vertical asymptotes f ( x) = 15
x 2 − 3 x − 10 *factor the denominator
So.. (x-5)(x+2)
x=5, x=-2 <---- 2 vertical asymptotes 1. Make sure the function is in lowest terms
2. Factor or use quadratic formula
3. Set to y=0 to find vertical asymptotes Def: The line y = b is a horizontal asymptote for the
graph of a rational function, f(x), if the value of f(x)
approaches the value ‘b’ as x approaches ± ∞ . Ex. Consider the following function:
x
-10000 -4000 -2000 -1000 -500 0
500 1000 2000 4000
f(x) .7501 .7504 .7507 .7514 .7529 -.3333 .7471 .7486 .7493 .7496 Locating horizontal asymptotes:
We want to look at the end behavior...

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