Question

Identify the vertical asymptote(s) of the function. Mr001-1. Jpg x = -4 x = -2 x = -1 x = 1 x = 2 x = 4.

Answer 1

Using it's concept, it is found that the vertical asymptotes of the function $f(x) = \frac{x + 2}{x^2 - 3x - 4}$ 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:

$f(x) = \frac{x + 2}{x^2 - 3x - 4}$

The denominator is $x^2 - 3x - 4$, which is a quadratic function with coefficients $a = 1, b = -3, c = -4$, hence, it's roots are found as follows.

$\Delta = b^2 - 4ac = (-3)^2 - 4(1)(-4) = 25$

$x_{1} = \frac{-(-3) + \sqrt{25}}{2} = 4$

$x_{2} = \frac{-(-3) - \sqrt{25}}{2} = -1$

Hence, the asymptotes are x = 4 and x = -1.

You can learn more about vertical asymptotes at brainly.com/question/11598999