The rational function that is represented by the given graph is [tex]f(x) = \frac{4x - 8}{x^{2} +x-6}[/tex]
What is a polynomial function ?
Rational function is any function that can be defined by a rational fraction, which is an algebraic fraction such that both the numerator and the denominator are polynomials.
We need to find out which rational function is represented by this graph.
Firstly, we see that graph does not exist at x = -3 and x = 2.
Thus, (x+3) and (x-2) cannot be equal to 0.
(x + 3)(x - 2) = x² + x - 6
Thus, the denominator of the function is x² + x - 6.
So, our solution can be B. or D.
We can also see that there is a circle over the graph at x = 2. This means that f(x) is undefined at x = 2. It is possible only if f(x) = ∞/∞ or 0/0 at x = 2.
On putting the value of x = 2 in both B. and D., we find that in D. f(x) = 0/0 at x = 2.
[tex]f(2) = \frac{4*2 - 8}{4 + 2 - 6} = \frac{0}{0}[/tex]
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