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
