Question

question 3 (multiple choice worth 2 points) (04.03r mc) given $f(x) = \frac{8x + 1}{2x - 9}$, what is the end behavior of the function? as $x \to -\infty$, $f(x) \to 9$; as $x \to \infty$, $f(x) \to 9$. as $x \to -\infty$, $f(x) \to -9$; as $x \to \infty$, $f(x) \to -9$. as $x \to -\infty$, $f(x) \to -4$; as $x \to \infty$, $f(x) \to -4$. as $x \to -\infty$, $f(x) \to 4$; as $x \to \infty$, $f(x) \to 4$.

Explanation:

Step1: Identify degrees of numerator/denominator

Numerator degree = 1, denominator degree = 1 (same degree).

Step2: Find horizontal asymptote

For same degrees, asymptote = ratio of leading coefficients: $\frac{8}{2}=4$.

Step3: Determine end behavior

As $x→±∞$, $f(x)$ approaches the horizontal asymptote 4.

Answer:

D. As x → -∞, f(x) → 4; as x → ∞, f(x) → 4.