the graph of the rational function f(x)=x²/(x² - 4) has no horizontal asymptote. true false

Answer:

B. False

Explanation:

Step1: Recall horizontal - asymptote rule

For a rational function $f(x)=\frac{a_nx^n+\cdots+a_0}{b_mx^m+\cdots + b_0}$, when $n = m$, the horizontal asymptote is $y=\frac{a_n}{b_m}$.

Step2: Identify $n$ and $m$ for $f(x)=\frac{x^2}{x^2 - 4}$

Here, $n = 2$ (degree of numerator), $m = 2$ (degree of denominator), $a_n=1$, $b_m = 1$.

Step3: Find the horizontal asymptote

Since $n=m = 2$, the horizontal asymptote is $y=\frac{1}{1}=1$. So the statement is false.