Questions: Consider the function graphed at right. The function has a minimum of -4. The function is increasing on the interval(s): The function is decreasing on the interval(s):

Consider the function graphed at right.

The function has a minimum of -4.

The function is increasing on the interval(s):

The function is decreasing on the interval(s):

Transcript text: Consider the function graphed at right. The function has a minimum of $-4$. The function is increasing on the interval(s): $\square$ The function is decreasing on the interval(s): $\square$

Solution

Solution Steps

Step 1: Identify the minimum point

The graph shows a parabola opening upwards, indicating a minimum point. The minimum value of the function is given as -4.

Step 2: Determine the x-coordinate of the minimum point

From the graph, the minimum value of -4 occurs at $ x = -2 $.

Step 3: Identify the intervals where the function is increasing and decreasing

The function is increasing on the interval where the graph moves upwards. This occurs to the right of the minimum point, i.e., $ x > -2 $.
The function is decreasing on the interval where the graph moves downwards. This occurs to the left of the minimum point, i.e., $ x < -2 $.