The graph shown here is the graph of which of the following rational functions ?

The first thing you should do for this case is to study the domain of the function to verify the values of x for which it is defined.
We have then the domain of the function is:
x = (- inf, -1)
x = (- 1, 3)
x = (3, inf)
Equivalently all the x that belong to:
(-inf, -1) U (-1, 3) U (3, inf)
Therefore, the function is:
F (x) = (x-2) / ((x + 1) * (x-3))
answer
A. F (x) = (x-2) / ((x + 1) * (x-3))

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shirleywashington shirleywashington · Answer 2 · 2019-07-04T12:33:59+02:00

Answer:

The correct options is (A) [tex]f(x) = \frac{x-2}{(x+1)(x-3)}[/tex]

Step-by-step explanation:

Consider the provided graph:

The provided graph has vertical asymptotes at x = -1 and x = 3.

Therefore, denominator must contain x + 1 and x - 3.

Also, at x = 2 the graph intersect the x axis that means at x = 2, y = 0

Therefore, the rational function must contain x - 2 in numerator.

Hence, the correct options is (A) because it contain x + 1 and x - 3 in denominator and x - 2 in numerator.