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Sagot :
Using it's concept, it is found that the vertical asymptotes of the function [tex]f(x) = \frac{x + 2}{x^2 - 3x - 4}[/tex] are given by:
- x = -1.
- x = 4.
Vertical asymptote:
- The vertical asymptotes of a function f(x) are the values of x which are outside the domain of the function.
- In a fraction, it is the roots of the denominator.
In this problem, the function is:
[tex]f(x) = \frac{x + 2}{x^2 - 3x - 4}[/tex]
The denominator is [tex]x^2 - 3x - 4[/tex], which is a quadratic function with coefficients [tex]a = 1, b = -3, c = -4[/tex], hence, it's roots are found as follows.
[tex]\Delta = b^2 - 4ac = (-3)^2 - 4(1)(-4) = 25[/tex]
[tex]x_{1} = \frac{-(-3) + \sqrt{25}}{2} = 4[/tex]
[tex]x_{2} = \frac{-(-3) - \sqrt{25}}{2} = -1[/tex]
Hence, the asymptotes are x = 4 and x = -1.
You can learn more about vertical asymptotes at https://brainly.com/question/11598999
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