Chapter 4: Q. 54 (page 225)

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$F (x) = \frac{x^{4} - 16}{x^{2} - 2 x}$

Short Answer

Expert verified

The given rational expression does not have a horizontal or oblique asymptote.

Step by step solution

Step 1. Given information

Given rational expression:

$F (x) = \frac{x^{4} - 16}{x^{2} - 2 x}$

Step 2. Write the concept

If $n \geq m + 2$ (the degree of the numerator is two or more greater than the degree of the denominator),

the quotient obtained is a polynomial of degree 2 or higher, and R has neither a horizontal nor an oblique

asymptote. In this case, for very large values of $|x|$ , the graph of R will behave like the graph of the

quotient.

Step 3. Calculation

here $n = 4, m = 2$

Thus, $n \geq m + 2$

Therefore no horizontal or oblique asymptote.

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Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$F (x) = \frac{x^{4} - 16}{x^{2} - 2 x}$

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the concept

Step 3. Calculation

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Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.F(x)=x4-16x2-2x

Short Answer

Step by step solution

Step 1. Given information

Step 2. Write the concept

Step 3. Calculation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Pure Maths

Applied Mathematics

Discrete Mathematics

Probability and Statistics

Theoretical and Mathematical Physics

Geometry

Study anywhere. Anytime. Across all devices.

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$F (x) = \frac{x^{4} - 16}{x^{2} - 2 x}$