Find the horizontal asymptote of each function.f(x)=8x2+12x2−x−6f\left(x\right)=\frac{8x^2+1}{2x^2-x-6}f(x)=2x2−x−68x2+1

Horizontal Asymptote at y = 4 y=4 y = 4

Find the horizontal asymptote of each function. f ( x ) = 8 x 2 + 1 2 x 2 − x − 6 f\left(x\right)=\frac{8x^2+1}{2x^2-x-6} f ( x ) = 2 x 2 − x − 6 8 x 2 + 1

In this problem, we're asked to find the horizontal asymptote of the function f of x is equal to 8x squared plus 1 over 2x squared minus x minus 6. So looking at the degree of the numerator and the denominator here, the degree of my numerator is 2, and the degree of my denominator is also 2. So that tells me that these degrees are equal to each other, which I now need to divide my leading coefficients here. So taking a look at my leading coefficients, I have 8 and 2. So my leading coefficient of my numerator divided by the leading coefficient of my denominator, 8 over 2, will give me a horizontal asymptote at y equals 4. I'll see you in the next video.

Find the horizontal asymptote of each function. f ( x ) = 8 x 2 + 1 2 x 2 − x − 6 f\left(x\right)=\frac{8x^2+1}{2x^2-x-6} f ( x ) = 2 x 2 − x − 6 8 x 2 + 1

Horizontal Asymptote at y = 4 y=4 y = 4

Horizontal Asymptote at y = 0 y=0 y = 0

Horizontal Asymptote at y = 1 4 y=\frac14 y = 4 1

5. Rational Functions

Asymptotes

Precalculus

5. Rational Functions

Asymptotes

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Multiple Choice

Find the horizontal asymptote of each function.
$f\left(x\right)=\frac{8x^2+1}{2x^2-x-6}$

Horizontal Asymptote at $y=0$

Horizontal Asymptote at $y=\frac14$

Horizontal Asymptote at $y=4$

Verified step by step guidance

Identify the degrees of the polynomials in the numerator and the denominator. The degree of the numerator is 2 (from 8x^2), and the degree of the denominator is also 2 (from 2x^2).

Since the degrees of the numerator and the denominator are equal, the horizontal asymptote is determined by the ratio of the leading coefficients.

The leading coefficient of the numerator is 8, and the leading coefficient of the denominator is 2.

Divide the leading coefficient of the numerator by the leading coefficient of the denominator to find the horizontal asymptote: $ \frac{8}{2} $.

The horizontal asymptote is $ y = 4 $.

6:24m

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Struggling with Precalculus?

Find the horizontal asymptote of each function.f(x)=8x2+12x2−x−6f\left(x\right)=\frac{8x^2+1}{2x^2-x-6}f(x)=2x2−x−68x2+1​

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Find the horizontal asymptote of each function.
$f\left(x\right)=\frac{8x^2+1}{2x^2-x-6}$