Exploring Piecewise Functions from Graphs

The video tutorial introduces piecewise functions, explaining how they are defined over different intervals. It uses a graph to illustrate the concept, showing how the function behaves in each interval. The tutorial covers three intervals, explaining the function's value and the importance of open and closed circles in defining these intervals. The video emphasizes the need for a function to be defined at only one point in each interval to maintain its validity.

What is a piecewise function?

• A function defined by a single equation.

• A function that is always increasing.

• A function that is always decreasing.

• A function defined by multiple equations over different intervals.

In the first interval, what is the value of the function?

• 6

• 0

• -9

• -5

Why is it important that -9 is not included in the first interval?

• Because the function would be increasing.

• Because the function would be constant.

• Because the function would be defined at two places.

• Because the function would be undefined.

What is the value of the function in the second interval?

• 6

• -9

• -7

• 0

Why is it important that -5 is not included in the second interval?

• Because the function would be undefined.

• Because the function would be defined at two places.

• Because the function would be constant.

• Because the function would be decreasing.

What is the value of the function at x = -5?

• 6

• -9

• -7

• 0

What is the value of the function in the third interval?

• -7

• 0

• -9

• 6

Why is it important that -1 is not included in the third interval?

• Because the function would be constant.

• Because the function would be defined at two places.

• Because the function would be undefined.

• Because the function would be increasing.

What is the value of the function at x = 9?

• -9

• 0

• 6

• -7

What is the purpose of function notation in piecewise functions?

• To make the function more complex.

• To make the function constant.

• To make the function undefined.

• To clearly define the function over different intervals.