Question

what are all the intervals in which the function is decreasing? 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. the function is decreasing when x is between 0.5 and 4 and when x is between 7 and 10. the function is decreasing when x is between -5 and -3 and when x is between 7 and 10. 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.

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

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.

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.