Question

Which rational functions have an oblique asymptote?Check all that apply.

Answer 1

Answer:

f(x) = (x² + 1)/x has an oblique asymptote ⇒ A

f(x) = (4x² - 6)/(x + 1) has an oblique asymptote ⇒ B

f(x) = x^5/(x³ + 1) has an oblique asymptote ⇒ D

f(x) = (x³ + 2)/(x² + 3x) has an oblique asymptote ⇒ F

Step-by-step explanation:

An oblique asymptote occurs when the polynomial in the numerator is a higher degree than the polynomial in the denominator

By using the definition above to find the rational function which has an oblique asymptote

∵ f(x) = (x² + 1)/x

∵ The highest degree of the numerator is 2

∵ The highest degree of the denominator is 1

- That means the numerator is a higher degree than the denominator

∴ f(x) = (x² + 1)/x has an oblique asymptote

∵ f(x) = (4x² - 6)/(x + 1)

∵ The highest degree of the numerator is 2

∵ The highest degree of the denominator is 1

- That means the numerator is a higher degree than the denominator

∴ f(x) = (4x² - 6)/(x + 1) has an oblique asymptote

∵ f(x) = x^5/(x³ + 1)

∵ The highest degree of the numerator is 5

∵ The highest degree of the denominator is 3

- That means the numerator is a higher degree than the denominator

∴ f(x) = x^5/(x³ + 1) has an oblique asymptote

∵ f(x) = (x³ + 2)/(x² + 3x)

∵ The highest degree of the numerator is 3

∵ The highest degree of the denominator is 2

- That means the numerator is a higher degree than the denominator

∴ f(x) = (x³ + 2)/(x² + 3x) has an oblique asymptote

Answer 2

Answer:

a, b, f

Step-by-step explanation:

i hope this helps