Question

A 2-column table with 9 rows. The first column is labeled x with entries negative 4, negative 3, negative 2, negative 1, 0, 1, 2, 3, 4. The second column is labeled f of x with entries 18, 9, 6, 3, 0, negative 3, negative 6, negative 9, negative 18. 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

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

Explanation:

Given the values in the table:

`\left|\begin{array}cx&f(x)\\--&--\\-4&18\\-3&9\\-2&6\\-1&3\\0&0\\1&-3\\2&-6\\3&-9\\4&-18\end{array}\right|`

We observe from the table that:

As x increases, the value of f(x) decreases

• i.e. Over time, when x → ∞, f(x) → –∞

As x decrease, the value of f(x) increases

• Similarly, when x → –∞, f(x) → ∞.

Therefore: that which best predicts the end behavior of the graph of f(x) is:

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