The figure below shows the graph of a rational function f. It has vertical asymp

Question

The figure below shows the graph of a rational function f. It has vertical asymptotes x= -2 and x = -6, and horizontal asymptote y = 0. The graph does not have an x-intercept, and it passes through the point (-7, 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. F(x) = a/x - b f(x) = a (x - b)/x - c f(x) = a/(x - b)(x - c) f(x) = a(x - b)/(x - c)(x - d) f(x) = a(x - b)(x - c)/(x - d)(x - c)

Explanation / Answer

Here we have the following given form :

Here in option a , we can see that we have only one vertical asymptotes , but in question we are given two vertical asymptotes so we neglect that option

In option b )  , we can see that we have only one vertical asymptotes and no x intercept

In option d) we can see that it has x intercept at x = b but in question it is given that graph has no x intercept

In option e) we can see that it has x intercept at x = b and x = c but in question it is given that graph has no x intercept

So we choose option C

f(x) = a/ ( x-b) ( x-c)

as it has two vertical asymptotes and

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