what is the end behavior of f(x)= (2x + 3)/(x - 1) as x approaches negative infinity? a f(x) approaches 1 b…

Explanation:

Step1: Divide numerator and denominator by x

Divide each term in $\frac{2x + 3}{x - 1}$ by $x$: $\frac{\frac{2x}{x}+\frac{3}{x}}{\frac{x}{x}-\frac{1}{x}}=\frac{2+\frac{3}{x}}{1 - \frac{1}{x}}$.

Step2: Evaluate limits as x approaches negative infinity

As $x\to-\infty$, $\lim_{x\to-\infty}\frac{3}{x}=0$ and $\lim_{x\to-\infty}\frac{1}{x}=0$. Then $\lim_{x\to-\infty}\frac{2+\frac{3}{x}}{1-\frac{1}{x}}=\frac{2 + 0}{1-0}$.

Step3: Calculate the result

$\frac{2+0}{1 - 0}=2$.

Answer:

B. $f(x)$ approaches 2