Question

Find the open interval(s) where the following function is increasing, decreasing, or constant. Express your answer in interval notation.Selecting an option will display any text boxes needed to complete your answer.- Increasing on one interval - Decreasing on one interval - Constant on one interval - Increasing on one interval- Decreasing on another - Increasing on two intervals - Decreasing on two intervals

Answer 1

ANSWER and EXPLANATION

We are given the graph in the picture.

We want to find the following intervals:

- Interval where the function is increasing

- Interval where the function is decreasing

- Interval where the function is constant.

To do that, first, we have to note that the domain of the function in the graph (the set of x values) is from negative infinity to positive infinity.

We know this because of the arrows on the line that point upward, that tell us that the function continues.

INTERVAL WHERE FUNCTION IS DECREASING

This is the interval with which the y value of the function drops.

If we examine it very closely, we see that the interval where the function is decreasing is:

$-\text{ }\infty\text{ < x }\leq\text{ 2.5}$

Because the y value starts dropping from negative infinity (already stated) and drops until it becomes constant at 2.5

INTERVAL WHERE FUNCTION IS CONSTANT

This is the interval with which the y value of the function is constant.

If we examine closely, we see that the function is constant over the interval:

$2.5\text{ }\leq\text{ x }\leq3.5$

INTERVAL WHERE FUNCTION IS INCREASING

This is the interval with which the y value of the function is rising.

If we examine closely, we will see that the function increases over the interval:

$3.5\text{ }\leq\text{ x }\leq\text{ }\infty$

The function increases over one interval, decreases over one interval and is constant over one interval.