Question

State the vertical asymptote of the rational function.

f(x)=(x-8)(x+4)/x^2-9

help me please and show work

Answer 1

Answer on Question #43005 – Math - Calculus

Task:

State the vertical asymptote of the rational function $f(x) = \frac{(x - 8)(x + 4)}{x^2 - 9}$.

help me please and show work.

Solution:

In practice, the vertical asymptotes are found quite easily. These points are zeros of the denominator of function $f(x)$.

The vertical asymptote is a vertical line. Its equation is $x = a$. That is, when $x$ tends to $a$ (from the right or from the left), the function tends to infinity (positive or negative).

$$x^2 - 9 = 0$$

So, $\begin{bmatrix} x_1 = 3 \\ x_2 = -3. \end{bmatrix}$ These are the vertical asymptotes of function $f(x) = \frac{(x - 8)(x + 4)}{x^2 - 9}$.

Answer:

$\begin{bmatrix} x_1 = 3 \\ x_2 = -3. \end{bmatrix}$ - vertical asymptotes.

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