SOLUTION: a)find any slant or vertical asymptotes. b)Graph y = f(x). Show all asymptotes. f(x) = 4^2 + x - 2/(4x

SOLUTION: a)find any slant or vertical asymptotes. b)Graph y = f(x). Show all asymptotes. f(x) = 4^2 + x - 2/(4x - 3)

Question 424225: a)find any slant or vertical asymptotes.
b)Graph y = f(x). Show all asymptotes.
f(x) = 4^2 + x - 2/(4x - 3)
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
a)find any slant or vertical asymptotes.
b)Graph y = f(x). Show all asymptotes.
f(x) = 4^2 + x - 2/(4x - 3)
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I will assume you meant the given equation to be written as follows:
f(x)=(4x^2+x-2)/(4x-3)
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To find the vertical asymptote for rational expressions, set the denominator=0, then solve for x.
4x-3=0
4x=3
x=3/4 (this is the vertical asymptote for this function)
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Because the degree of the numerator is higher than the denominator, you will have a slant asymptote for this function. (Note:If the degree of the numerator
is less than that of the denominator,the x-axis becomes the horizontal asymptote. If the degrees are the same, the quotient of the lead coefficient of the denominator divided by the lead coefficient of the numerator becomes the horizontal asymptote.)
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To find the slant asymptote for given function, divide numerator,by denominator.
by long division and you will get a quotient and a remainder. The quotient is an equation of a straight line which is your asymptote.
(4x^2+x-2)/(4x-3)=(x+1)+remainder,3/(4x-3)
The graph below might help you understand this problem a little better.
..

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