The rational function that matches with the graph of the picture is f(x) = (2 · x + 7.2)/(x + 3).
What is the rational function behind the graph seen in the picture?
Herein we have the graph of a rational function of the form f(x) = p(x)/q(x) . The domain of these kind of functions is all real numbers except those values of x such that q(x) = 0. Graphically speaking, there is a vertical asymptote when a discontinuity exists and an horizontal asymptote for x → ± ∞.
In accordance with the picture, there are one horizontal asymptote and one vertical asymptote. As the horizontal asymptote of the function is distinct of 0, then the grade of p(x) is the same grade of q(x). Therefore, we have a rational function of the form:
f(x) = (2 · x + k)/(x + 3) (1)
If we know that x = 0 and y = 2.4, then the value of k is:
2.4 = (2 · 0 + k)/(0 + 3)
2.4 = k/3
k = 7.2
Therefore, the rational function that matches with the graph of the picture is f(x) = (2 · x + 7.2)/(x + 3).
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