4. f(x) = (x - 2)/(2x + 1) find the horizontal asymptote. y = -2 none y = 0 y = 1/2

Explanation:

Step1: Recall the rule for horizontal asymptote of rational functions

For a rational function $f(x)=\frac{a_nx^n+\cdots+a_0}{b_mx^m+\cdots + b_0}$, if $n = m$, the horizontal - asymptote is $y=\frac{a_n}{b_m}$. Here, for $f(x)=\frac{x - 2}{2x+1}$, the degree of the numerator $n = 1$ and the degree of the denominator $m = 1$.

Step2: Identify the leading - coefficients

The leading coefficient of the numerator $a_n = 1$ (the coefficient of $x$ in $x - 2$) and the leading coefficient of the denominator $b_m=2$ (the coefficient of $x$ in $2x + 1$).

Step3: Calculate the horizontal asymptote

Using the formula $y=\frac{a_n}{b_m}$, we have $y=\frac{1}{2}$.

Answer:

D. $y = \frac{1}{2}$