Mathematics, 10.04.2020 21:50 arteria3

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

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Answer from: aksambo4707

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 from: Quest

There would be 36.35 pounds

Answer from: Quest

First step is to get rid of the square root. remember that a square root is the same as raising to the (1/2) power. see below: $\sqrt{\frac{ {72x}^{16} }{ {50x}^{{{36} }}}} = \frac{ { \sqrt{72}x}^{ {16}^{ (\frac{1}{2}) } } }{ { \sqrt{50} x}^ {{36}^{ (\frac{1}{2}) } }}$ multiply exponents per exponent rules to get: $\frac{ { \sqrt{72}x}^{8} }{ { \sqrt{50}x}^{18} }$ remember you subtract exponents from the denominator and add exponents in the numerator so: $\sqrt{ \frac{72}{ 50}} \times ( {x}^{(8 - 18) } ) = \sqrt{ \frac{36}{25} } \times ( {x}^{ - 10} )$ simplify further: $\frac{6}{5} {x}^{ - 10} = \frac{6}{5 {x}^{10} }$ so a is the correct choice. if you don't understand this google exponent rules and it will you understand. look at the image results.
Plz hurrywhat is the simplified form of ? assume x ≠ 0.

Plz hurrywhat is the simplified form of  ? assume  x  ≠ 0.

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