Question

A 2-column table with 9 rows. The first column is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3. The second column is labeled f of x with entries negative 6, negative 2, 0, 4, 4, 0, negative 2, negative 6, negative 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) → –∞.

Answer 1

As x → ∞, f(x) → −∞, and as x → −∞, f(x) → −∞.

Reason: For positive x the values fall (f(1)=−2, f(2)=−6, f(3)=−10) so the right end goes to −∞. For negative x the values also fall as we go left from −1 (f(−1)=4, f(−2)=4, f(−3)=0, f(−4)=−2, f(−5)=−6), so the left end also trends downward toward −∞.