what are all the intervals in which the function is decreasing? the function is decreasing when x is between…

Answer:

To determine the intervals where the function is decreasing, we need to analyze the graph. A function is decreasing when, as (x) increases, (y) decreases.

Looking at the options:

• Option 1: The function is decreasing when (x) is between - 5 and - 3, when (x) is between 0.5 and 4, and when (x) is between 7 and 10.
• Option 2: The function is decreasing when (x) is between 0.5 and 4 and when (x) is between 7 and 10.
• Option 3: The function is decreasing when (x) is between - 5 and - 3 and when (x) is between 7 and 10.
• Option 4: The function is decreasing when (x) is between - 7 and 2, when (x) is between - 7 and 4.25, and when (x) is between - 3.5 and - 2.

We assume we have visually inspected the graph. If the graph shows that the function is decreasing in the intervals (x\in(-5,-3)), (x\in(0.5,4)) and (x\in(7,10)), the correct answer is: The function is decreasing when (x) is between - 5 and - 3, when (x) is between 0.5 and 4, and when (x) is between 7 and 10.

Explanation:

Step1: Recall decreasing - function definition

A function (y = f(x)) is decreasing on an interval if for any two points (x_1) and (x_2) in the interval with (x_1<x_2), we have (f(x_1)>f(x_2)).

Step2: Analyze the graph visually

Look at the given graph of the function and identify the intervals where the curve is going down - ward as we move from left - to - right.

Step3: Match with options

Compare the intervals identified from the graph with the intervals given in each option to find the correct one.