The correct statement regarding the limit, using asymptotes, is:
The function [tex]f(x) = \frac{28x - 10x^2}{4x^2 - 1}[/tex] has a horizontal asymptote at [tex]y = -\frac{5}{2}[/tex].
What are the asymptotes of a function f(x)?
- The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
- The horizontal asymptote is the limit of f(x) as x goes to infinity, as long as this value is different of infinity.
In this problem, we have a limit, which is associated with a horizontal asymptote. The limit is:
[tex]\lim_{x \rightarrow \infty} \frac{28x - 10x^2}{4x^2 - 1}[/tex]
x goes to infinity, hence we consider only the highest exponents.
[tex]\lim_{x \rightarrow \infty} \frac{28x - 10x^2}{4x^2 - 1} = \lim_{x \rightarrow \infty} -\frac{10x^2}{4x^2} = -\frac{10}[4} = -\frac{5}{2}[/tex]
Hence the correct statement is:
The function [tex]f(x) = \frac{28x - 10x^2}{4x^2 - 1}[/tex] has a horizontal asymptote at [tex]y = -\frac{5}{2}[/tex].
More can be learned about asymptotes at https://brainly.com/question/16948935
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