Question

Use the graph of the piecewise function to answer the question.

Over which intervals is the function decreasing?

Select all that apply.

x > 6

x ≤ -6

1 < x ≤ 5

-5 < x ≤ 1

5 < x ≤ 6

-6 < x ≤ -5​

Answer 1

The decreasing interval of the function are x ≤ -6, 1 < x ≤ 5 and x > 6

How to determine the decreasing interval?

From the given graph, the function value decrease at the following x values

• Negative infinity to x = -6
• x = 1 to x = 5
• x = 6 to x = infinity

This can be properly represented as:

x ≤ -6, 1 < x ≤ 5 and x > 6

Hence, the decreasing interval of the function are x ≤ -6, 1 < x ≤ 5 and x > 6

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