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Find a function y = f(x) that has only one horizontal asymptote and
exactly 2021 vertical asymptotes. You have to clearly write the formula for f(x) for 2
marks and explain carefully why your function satisfies the given condition for 3 marks.
A sketch of the graph is recommended but it is not enough for your explanation

Sagot :

Using asymptote concepts, it is found that the function is:

[tex]f(x) = \frac{10x^2}{x^2 + 2x - 3}[/tex]

  • First we find the vertical asymptotes, which are the values for which the function is outside the domain.
  • We consider a fraction, thus, deciding to place vertical asymptotes at [tex]x = -1[/tex] and at [tex]x = 3[/tex], the denominator is:

[tex](x + 1)(x - 3) = x^2 + 2x - 3[/tex]

  • The horizontal asymptote is the limit of f(x) as x goes to infinity. We suppose it is 10, thus the numerator is [tex]10x^2[/tex], as it has to be the same degree of the denominator.

Which means that the function is:

[tex]f(x) = \frac{10x^2}{x^2 + 2x - 3}[/tex]

The graph is sketched below.

A similar problem is given at https://brainly.com/question/17375447

View image Joaobezerra
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