Question

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

Answer 1

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))

Answer 2

Answer:

The correct options is (A) $f(x) = \frac{x-2}{(x+1)(x-3)}$

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.