Question

list the interval(s) on which f is increasing. the interval(s) on which f is increasing is/are. (type your answer in interval notation. use a comma to separate answers as needed.)

Explanation:

To determine the intervals where the function \( f(x) \) is increasing, we analyze the graph by observing the direction of the curve as \( x \) increases. A function is increasing on an interval if, as \( x \) moves from left to right (increases), the \( y \)-values (function values) also increase.

Step 1: Identify Increasing Segments

Looking at the graph:

• From \( x = -12 \) to \( x = -10 \): The graph rises ( \( y \)-values increase as \( x \) increases).
• From \( x = 4 \) to \( x = 6 \): The graph rises ( \( y \)-values increase as \( x \) increases).

Step 2: Express Intervals in Interval Notation

• For \( x = -12 \) to \( x = -10 \): The interval is \( [-12, -10] \) (since the endpoints are included, as indicated by the solid dots).
• For \( x = 4 \) to \( x = 6 \): The interval is \( [4, 6] \) (endpoints included).

Answer:

\([-12, -10], [4, 6]\)