which line represents a horizontal asymptote of f(x)=-(5x^2 - 3x + 2)/(10x^2 - 1)? y=-2 y=-0.5 y=0.5 y=2

Explanation:

Step1: Identify degree of polynomials

The degree of the numerator $5x^{2}-3x + 2$ and denominator $10x^{2}-1$ is 2.

Step2: Use horizontal - asymptote rule

For a rational function $\frac{f(x)}{g(x)}$ where $\text{deg}(f)=\text{deg}(g)=n$, the horizontal asymptote is $y = \frac{a_{n}}{b_{n}}$, where $a_{n}$ and $b_{n}$ are the leading coefficients of $f(x)$ and $g(x)$ respectively. Here $a_{n}=- 5$ and $b_{n}=10$.

Step3: Calculate the value of the horizontal asymptote

$y=\frac{-5}{10}=-0.5$

Answer:

B. $y = - 0.5$