Question

determine if the function is increasing, decreasing, or constant for the following intervals of x.
interval\tincreasing\tdecreasing\tconstant
-1<x<3
3<x<5
5<x<7
x>7

Explanation:

Step1: Recall function behavior rules

A function is increasing when the \(y -\)values increase as \(x\) increases, decreasing when \(y -\)values decrease as \(x\) increases, and constant when \(y -\)values stay the same as \(x\) changes.

Step2: Analyze \(x < - 3\)

As \(x\) moves from left (lesser values) to right (towards - 3) on the graph, the \(y -\)values are going down, so it's decreasing.

Step3: Analyze \(-3

As \(x\) increases from - 3 to 3, the \(y -\)values are going up, so it's increasing.

Step4: Analyze \(3

As \(x\) increases from 3 to 7, the \(y -\)values are going down, so it's decreasing.

Step5: Analyze \(x > 7\)

As \(x\) increases (moves to the right of 7), the \(y -\)values are going up, so it's increasing.

Answer:

Interval	Increasing	Decreasing	Constant
\(-3	Yes	No	No
\(3	No	Yes	No
\(x > 7\)	Yes	No	No