The vertical and the horizontal asymptotes of the function [tex]f(x) = \frac{2x^2 +7x - 4}{x^2 + 5x + 4}[/tex] are x = -1, and y = 2
The function is given as:
[tex]f(x) = \frac{2x^2 +7x - 4}{x^2 + 5x + 4}[/tex]
To start with, we plot the graph of f(x)
The asymptotes are the lines that pass through the points that appears to be on the curve because of their nearness to the curve, but they are actually not on the curve of the function.
From the graph (see attachment), we can see that:
The vertical and the horizontal asymptotes are x = -1, and y = 2
Read more about asymptotes at:
https://brainly.com/question/8493280