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

The best prediction is

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

What is interval?

An interval is a set of real numbers between two given numbers called the endpoints of the interval.

Given:

x  f(x)

-4  18

-3  9

-2  6

-1  3

0  0

1  -3

2  -6

3  -9

4  -18

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

i.e. Over time, when x → ∞, f(x) → –∞

and then x decrease, the value of f(x) increases

when x → –∞, f(x) → ∞.

Hence, best predicts the end behavior of the graph of f(x) is x → ∞, f(x) → –∞, and as x → –∞, f(x) → ∞.

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