Respuesta :
In the list of rational functions, 1st, 2nd, 4th, and 5th are the rational functions those have an oblique asymptote.
What is a function?
"A function from a set X to a set Y assigns to each element of X exactly one element of Y. The set X is called the domain of the function and the set Y is called the codomain of the function."
The given rational functions are:
1. [tex]f(x) = \frac{x^{2}+1}{x}[/tex]
As the degree of numerator(2) is greater than the degree of denominator(1), This function has an oblique asymptote.
2. [tex]f(x) = \frac{4x^{2}-6}{x+1}[/tex]
As the degree of numerator(2) is greater than the degree of denominator(1), This function has an oblique asymptote.
3. [tex]f(x) = \frac{-x}{x^{2} }[/tex]
As the degree of numerator(1) is less than the degree of denominator(2), This function does not have an oblique asymptote.
4. [tex]f(x) = \frac{x^{5}}{x^{3}+1}[/tex]
As the degree of numerator(5) is greater than the degree of denominator(3), This function has an oblique asymptote.
5. [tex]f(x)= \frac{x^{3}+2}{x^{2}+3x}[/tex]
As the degree of numerator(3) is greater than the highest degree of denominator(2), This function has an oblique asymptote.
Learn more about a function here: https://brainly.com/question/15642520
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