SOLUTION: The figure below shows the graph of a rational function f. It has vertical asymptotes x=-3 and x=4, and horizontal asymptote y=0. The graph does not have an x-intercept, and it pas
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-> SOLUTION: The figure below shows the graph of a rational function f. It has vertical asymptotes x=-3 and x=4, and horizontal asymptote y=0. The graph does not have an x-intercept, and it pas
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Question 1146685: The figure below shows the graph of a rational function f. It has vertical asymptotes x=-3 and x=4, and horizontal asymptote y=0. The graph does not have an x-intercept, and it passes through the point (3,1) The equation for f(x) has one of the five forms shown below. Choose the appropriate form for f(x), and then write the equation. You can assume that f(x) is in simplest form. Answer by greenestamps(13200) (Show Source):
Since you don't show the figure or the answer choices, you might take the trouble to rephrase the question....
(1) Since the graph has no x-intercept, the numerator of the rational function has no variables; it is just a constant.
(2) Note that (1) guarantees that the horizontal asymptote will be y=0.
(3) Vertical asymptotes at x=-3 and x=4 mean there are factors of (x+3) and (x-4) in the denominator.
(4) The factors of (x+3) and (x-4) in the denominator can be to any positive integer powers. Different combinations of those powers will require different values of the constant in the numerator in order to make the graph pass through (3,1).
Presumably only one of the answer choices shows only a constant in the numerator and factors of both (x+3) and (x-4) in the denominator.
Here are the graphs of two functions that satisfy the given conditions.
