Question

question 7 of 10
which of the following notations correctly describe the end behavior of the polynomial graphed below?
graph of a polynomial with x-axis from -8 to 8 and y-axis from -8 to 8, showing a curve with roots near -2, 0, and 2, and end behavior
a. \\( \

$$\begin{cases} x \\to -\\infty, f(x) \\to -\\infty \\\\ x \\to \\infty, f(x) \\to -\\infty \\end{cases}$$

\\)
b. \\( \

$$\begin{cases} x \\to -\\infty, f(x) \\to -\\infty \\\\ x \\to \\infty, f(x) \\to \\infty \\end{cases}$$

\\)
c. \\( \

$$\begin{cases} x \\to -\\infty, f(x) \\to \\infty \\\\ x \\to \\infty, f(x) \\to -\\infty \\end{cases}$$

\\)
d. \\( \

$$\begin{cases} x \\to -\\infty, f(x) \\to \\infty \\\\ x \\to \\infty, f(x) \\to \\infty \\end{cases}$$

\\)

Explanation:

Step1: Check end behavior as \(x \to -\infty\)

The graph rises upward as \(x\) goes left to negative infinity, so \(f(x) \to \infty\).

Step2: Check end behavior as \(x \to \infty\)

The graph rises upward as \(x\) goes right to positive infinity, so \(f(x) \to \infty\).

Answer:

D. \(x \to -\infty, f(x) \to \infty\); \(x \to \infty, f(x) \to \infty\)