Chapter 11: Q25. (page 731)

Identify the asymptotes of each function.
$y = \frac{2}{(x - 4) (x + 2)}$

Short Answer

Expert verified

The asymptotes of the given function are $x = 4$ , $x = - 2$ and $y = 0$ .

Step by step solution

Step 1. Define asymptotes.

An asymptote is a line that the graph of a function approaches.

Step 2. Set a denominator equal to zero.

Set a denominator of a given expression equal to zero.

$(x - 4) (x + 2) = 0$

Step 3. Simplify.

Simplify the above expression.

$\begin{array}{l} (x - 4) = 0 or (x + 2) = 0 \\ x = 4 x = - 2 \end{array}$

Therefore, the vertical asymptotes are $x = 4$ and $x = - 2$ . Horizontal asymptotes are $y = 0$ .

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$x$	1	4	8	12
$y$	2	8	16	24

Identify the asymptotes of each function.
$y = \frac{2}{(x - 4) (x + 2)}$

Short Answer

Step by step solution

Step 1. Define asymptotes.

Step 2. Set a denominator equal to zero.

Step 3. Simplify.

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Short Answer

Step by step solution

Step 1. Define asymptotes.

Step 2. Set a denominator equal to zero.

Step 3. Simplify.

One App. One Place for Learning.

Most popular questions from this chapter

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Identify the asymptotes of each function.
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