The rational function with the given characteristics is [tex]f(x) = \frac{3x + 1}{x - 4} [/tex].
Any function that can be expressed mathematically as a rational fraction—an algebraic fraction in which both the numerator and the denominator are polynomials—is referred to as a rational function. The polynomials' coefficients don't have to be rational numbers,they can be found in any field K.
given that a vertical asymptote at x=-4.
A horizontal asymptote at y=3.
The denominator of the function cancels for this value and the numerator does not cancel at this value if the rational function has a vertical asymptote at x=4.
[tex]f(x) = \frac{p(x)}{(x - 4)} [/tex]
The degree of the numbered variable is equal to the degree of the denominator if the rational function has a horizontal asymptote at y=3, and the coefficient of the higher degree variable is three times larger.
Hence,
[tex]f(x) = \frac{3x + 1}{x - 4} [/tex]
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