A 2-column table with 8 rows. The first column is labeled x with entries negative 6, negative 5, negative 4, negative 3, negative 2, negative 1, 0, 1. The second column is labeled f of x with entries 34, 3, negative 10, negative 11, negative 6, negative 1, negative 2, negative 15.

Question

Using only the values given in the table for the function, f(x), what is the interval of x-values over which the function is increasing?

(–6, –3)
(–3, –1)
(–3, 0)
(–6, –5)

Answer 1

To determine the intervals where the function \( f(x) \) is increasing, we need to look for ranges of \( x \) where the values of \( f(x) \) are getting larger as \( x \) increases.

From the table:

• \( f(-6) = 34 \)
• \( f(-5) = 3 \) (decreasing from -6 to -5)
• \( f(-4) = -10 \) (decreasing from -5 to -4)
• \( f(-3) = -11 \) (decreasing from -4 to -3)
• \( f(-2) = -6 \) (increasing from -3 to -2)
• \( f(-1) = -1 \) (increasing from -2 to -1)
• \( f(0) = -2 \) (decreasing from -1 to 0)
• \( f(1) = -15 \) (decreasing from 0 to 1)

The function shows increases from \( -3 \) to \( -2 \) and from \( -2 \) to \( -1 \). Thus, we notice that:

• From \( x = -3 \) to \( x = -2 \), \( f(x) \) increases.
• From \( x = -2 \) to \( x = -1 \), \( f(x) \) increases.

Therefore, the overall increasing interval is from \( -3 \) to \( -1 \).

To express this as an interval, we can say \( (-3, -1) \) is where the function is increasing.

Thus, the correct answer is:

(–3, –1).