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math sec 4.6 rw

# P x f x if q x is a rational function in lowest terms

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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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