Question

determine if the function is increasing, decreasing, or constant for the following intervals of x. assume that x is increasing in each of the intervals. the graph of a function is shown below. intervals: -8 ≤ x ≤ -4, -4 ≤ x ≤ -2, 1 ≤ x ≤ 8, x > 8. table with columns increasing, decreasing, constant.

Explanation:

Step1: Analyze \(-8 \leq x \leq -4\)

As \(x\) increases from \(-8\) to \(-4\), the \(y\)-values rise. So, the function is increasing here.

Step2: Analyze \(-4 \leq x \leq -2\)

As \(x\) increases from \(-4\) to \(-2\), the \(y\)-values still rise (slope positive). So, the function is increasing here.

Step3: Analyze \(1 \leq x \leq 6\)

As \(x\) increases from \(1\) to \(6\), the \(y\)-value stays the same (horizontal line). So, the function is constant here.

Step4: Analyze \(x > 6\)

As \(x\) increases beyond \(6\), the \(y\)-values fall (slope negative). So, the function is decreasing here.

Answer:

• For \(-8 \leq x \leq -4\): Increasing (circle "Increasing")
• For \(-4 \leq x \leq -2\): Increasing (circle "Increasing")
• For \(1 \leq x \leq 6\): Constant (circle "Constant")
• For \(x > 6\): Decreasing (circle "Decreasing")