the graph of $f(x)=\frac{(6 - 4x)^2}{2x^2-5x + 12}$ has a horizontal asymptote at $y=square$.
the graph of $f(x)=\frac{(6 - 4x)^2}{2x^2-5x + 12}$ has a horizontal asymptote at $y=square$.
Answer
Answer:
8
Explanation:
Step1: Expand the numerator
$(6 - 4x)^2=36-48x + 16x^{2}$
Step2: Analyze the degrees of polynomials
The degree of the numerator $n = 2$ and degree of the denominator $m=2$.
Step3: Find the horizontal - asymptote
For a rational function $\frac{a_nx^n+\cdots+a_0}{b_mx^m+\cdots + b_0}$ with $n = m$, the horizontal asymptote is $y=\frac{a_n}{b_m}$. Here $a_n = 16$ and $b_m = 2$, so $y=\frac{16}{2}=8$.