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kudzordzifrancis

ANSWER

[tex]f(x) = \frac{ {x}^{2} }{ {x}^{2} + 1 } [/tex]

EXPLANATION

We write the function such that both the numerator and the denominator are prime.

An example of a rational function with no vertical asymptotes and no holes is

[tex]f(x) = \frac{ {x}^{2} }{ {x}^{2} + 1 } [/tex]

For the above rational function, the denominator is never zero, so there are no vertical asymptotes.

Also the highest common factor for the numerator and the denominator is 1 so there are no holes.

abidemiokin

An example of such a rational function with no vertical asymptotes and no holes is given as: h(x) = x²/x²-1

Vertical and Horizontal Asymptotes

According to the question, we were to write a rational function with no horizontal and Vertical asymptotes.

The function will be such that both the numerator and the denominator are prime.

An example of such a rational function with no vertical asymptotes and no holes is given as:

h(x) = x²/x²-1

For the above rational function, the denominator is never zero, so there are no vertical asymptotes.

Also the highest common factor for the numerator and the denominator is 1 so there are no holes.

Learn more on asymptote here; https://brainly.com/question/4138300

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