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
