select the correct answer. which statement describes the end - behavior of the function? $f(x)=\frac{x^{2}-10…

select the correct answer. which statement describes the end - behavior of the function? $f(x)=\frac{x^{2}-100}{x^{2}-3x - 4}$ a. the function approaches 0 as x approaches $-infty$ and $infty$. b. the function approaches 1 as x approaches $-infty$ and $infty$. c. the function approaches 5 as x approaches $-infty$ and $infty$. d. the function approaches 25 as x approaches $-infty$ and $infty$.

select the correct answer. which statement describes the end - behavior of the function? $f(x)=\frac{x^{2}-100}{x^{2}-3x - 4}$ a. the function approaches 0 as x approaches $-infty$ and $infty$. b. the function approaches 1 as x approaches $-infty$ and $infty$. c. the function approaches 5 as x approaches $-infty$ and $infty$. d. the function approaches 25 as x approaches $-infty$ and $infty$.

Answer

Explanation:

Step1: Analizar el grado de numerador y denominador

El numerador es $x^{2}-100$ (grado 2) y el denominador es $x^{2}-3x - 4$ (grado 2).

Step2: Dividir coeficientes de términos de mayor grado

Al dividir los coeficientes de los términos de mayor grado (ambos son 1 para $x^{2}$ en numerador y denominador), el límite cuando $x\to\pm\infty$ es 1.

Answer:

C. The function approaches 1 as x approaches $-\infty$ and $\infty$.