Question

x | f(x)
-5 | -6
-4 | -2
-3 | 0
-2 | 4
-1 | 4
0 | 0
1 | -2
2 | -6
3 | -10
based on the table, which best predicts the end behavior of the graph of f(x)?
○ as x → ∞, f(x) → ∞, and as x → -∞, f(x) → ∞.
○ as x → ∞, f(x) → ∞, and as x → -∞, f(x) → -∞.
○ as x → ∞, f(x) → -∞, and as x → -∞, f(x) → ∞.
○ as x → ∞, f(x) → -∞, and as x → -∞, f(x) → -∞.

Explanation:

Step1: Check left end trend

For \(x=-5,-4,-3\), \(f(x)=-6,-2,0\); as \(x\to-\infty\) (more negative), \(f(x)\) decreases (from -6 to lower values if trend continues).

Step2: Check right end trend

For \(x=1,2,3\), \(f(x)=-2,-6,-10\); as \(x\to\infty\) (more positive), \(f(x)\) decreases to more negative values.

Step3: Confirm end behavior

Both ends show \(f(x)\to-\infty\) as \(x\to\pm\infty\).

Answer:

As \(x \to \infty\), \(f(x) \to -\infty\), and as \(x \to -\infty\), \(f(x) \to -\infty\)