Question 737240: what is the vertical asymptote, horizontal asymptote, x-intercept, y-intercept, domain and range for f(x)=(5x^2+7x+2)/(2x^2-8)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! what is the vertical asymptote, horizontal asymptote, x-intercept, y-intercept, domain and range for f(x)=(5x^2+7x+2)/(2x^2-8)
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vertical asymptotes:
set denominator=0, then solve for x
2x^2-8=0
2x^2=8
x^2=4
x=±2
..
horizontal asymptotes: y=5/2 (when degree of numerator =degree of denominator, divide lead coefficient of numerator by lead coefficient of denominator)
..
x-intercept:
set y=0
numerator=0
5x^2+7x+2=0
at x=-1
and
at x=-0.4
..
y-intercept:
set x=0
y=2/-8=-1/4
..
domain: (-∞,-2) U (-2,2) U (2,∞)
range: (-∞,.06) U (5/2,∞)
number line:
<... +....-2..-...-1...+...-0.4...-...2..+...>
note: (-∞,.06) is approximate only
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