Questions: Consider the following rational function. f(x) = (x+2) / (x-10) Step 2 of 2: Find equations for the horizontal or oblique asymptotes, if any, for the function.

Consider the following rational function.
f(x) = (x+2) / (x-10)

Step 2 of 2: Find equations for the horizontal or oblique asymptotes, if any, for the function.

Transcript text: Consider the following rational function. \[ f(x)=\frac{x+2}{x-10} \] Step 2 of 2: Find equations for the horizontal or oblique asymptotes, if any, for the function.

Solution

Solution Steps

Step 1: Identify the Function

The given rational function is

\[ f(x) = \frac{x + 2}{x - 10} \]

Step 2: Determine the Degrees of the Numerator and Denominator

The degree of the numerator \(x + 2\) is 1, and the degree of the denominator \(x - 10\) is also 1. Since the degrees are equal, we can find the horizontal asymptote by taking the ratio of the leading coefficients.

Step 3: Calculate the Leading Coefficients

The leading coefficient of the numerator is 1, and the leading coefficient of the denominator is also 1. Therefore, the horizontal asymptote is given by:

\[ \text{Horizontal Asymptote} = \frac{\text{Leading Coefficient of Numerator}}{\text{Leading Coefficient of Denominator}} = \frac{1}{1} = 1.0 \]