SOLUTION: Find an equation of a rational function f that satisfies the given conditions.
vertical asymptotes: x = −3, x = 0
horizontal asymptote: y = 0
x-intercept: 3; f(4) = 1
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-> SOLUTION: Find an equation of a rational function f that satisfies the given conditions.
vertical asymptotes: x = −3, x = 0
horizontal asymptote: y = 0
x-intercept: 3; f(4) = 1
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Question 1113797: Find an equation of a rational function f that satisfies the given conditions.
vertical asymptotes: x = −3, x = 0
horizontal asymptote: y = 0
x-intercept: 3; f(4) = 1 Answer by greenestamps(13200) (Show Source):
Vertical asymptotes (values of x where the function is undefined -- i.e., has no value) are caused by factors in the denominator that are equal to 0. If there are asymptotes at x=-3 and x=0, then there are factors of (x+3) and x in the denominator.
(2) horizontal asymptote: y = 0
The horizontal asymptote is 0 if the degree of the numerator is less than the degree of the numerator. We'll come back to this one....
(3) x-intercept: 3
An x-intercept (where the function value is 0) is caused by a factor in the numerator that is equal to 0. If there is an x-intercept at x=3, there must be a factor of (x-3) in the numerator.
Note that the degree of the numerator at this point is less than the degree of the denominator; so the condition for having a horizontal asymptote of y=0 is satisfied. So we have all the factors of our rational function that contain variables; we now need to find the constant factor.
