Question

A 2-row table with 9 columns. The first row is labeled x with entries negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3. The second row is labeled f of x with entries negative 14, 6, 0, negative 4, negative 6, negative 6, negative 4, 0, 6.
Based on the table, which statement best describes a prediction for 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

Look at the matching pairs: f(-4)=f(3), f(-3)=f(2), f(-2)=f(1), f(-1)=f(0). That shows the graph is symmetric about x = -0.5, so the two ends have the same behavior. Since f(1)= -4, f(2)=0, f(3)=6 and the right side is increasing and goes positive, the ends must both go up.

Answer: As x → ∞, f(x) → ∞, and as x → –∞, f(x) → ∞.