Chapter 4: Q. 9 (page 247)

Write a function that meets the given conditions.
Rational function; asymptotes: $y = 2, x = 4$ , domain $\{x | x \neq 4, 9\}$

Short Answer

Expert verified

The possible rational function is $r (x) = \frac{2 x^{2}}{(x - 4) (x - 9)}$

Step by step solution

Step 1. Given Information

The given data is asymptotes $y = 2, x = 4$ : , domain $\{x | x \neq 4, 9\}$

Step 2. Explanation

From the given domain of the function, the denominator is 0 when $x = 4 a n d x = 9$

Thus, the factor of denominator can be written as $(x - 4) (x - 9)$

Since $y = 2$ , the ratio of the coefficients of the numerator and denominator is 2. since, the degree of the denominator is 2, the numerator must also have a degree of 2.

Thus, one possible choice of rational function is $r (x) = \frac{2 x^{2}}{(x - 4) (x - 9)}$

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Write a function that meets the given conditions.
Rational function; asymptotes: $y = 2, x = 4$ , domain $\{x | x \neq 4, 9\}$

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

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Write a function that meets the given conditions.Rational function; asymptotes:y=2,x=4, domainx|x≠4,9

Short Answer

Step by step solution

Step 1. Given Information

Step 2. Explanation

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

Mechanics Maths

Logic and Functions

Pure Maths

Statistics

Applied Mathematics

Discrete Mathematics

Study anywhere. Anytime. Across all devices.

Write a function that meets the given conditions.
Rational function; asymptotes: $y = 2, x = 4$ , domain $\{x | x \neq 4, 9\}$