Chapter 4: Q. 53 (page 225)

Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$G (x) = \frac{x^{4} - 1}{x^{2} - x}$

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:

$G (x) = \frac{x^{4} - 1}{x^{2} - x}$

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.
$G (x) = \frac{x^{4} - 1}{x^{2} - x}$

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.G(x)=x4-1x2-x

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

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Find the vertical, horizontal, and oblique asymptotes, if any, of each rational function.
$G (x) = \frac{x^{4} - 1}{x^{2} - x}$