Identifying Graph Intervals: Increasing, Decreasing, and Constant

The video tutorial by Mathemagical and Miss Muscarella explains how to determine where a graph is increasing, decreasing, or constant by analyzing the slopes. Positive slopes indicate increasing intervals, negative slopes indicate decreasing intervals, and zero slopes indicate constant intervals. The tutorial includes three examples to illustrate these concepts, emphasizing the use of x-values and soft brackets. Viewers are encouraged to practice identifying intervals on their own.

What does a positive slope indicate about a function?

• The function is undefined.

• The function is increasing.

• The function is constant.

• The function is decreasing.

Which type of brackets should be used when discussing increasing, decreasing, and constant intervals?

• Curly brackets

• Square brackets

• Soft brackets

• Angle brackets

In the first example, what is the interval where the function is increasing?

• From -5 to -2 and from 1 to 3

• From -2 to 1 and from 3 to 5

• From -5 to 1 and from 2 to 3

• From -3 to 0 and from 2 to 4

In the first example, what is the interval where the function is constant?

• From -5 to -2

• From 3 to 5

• From 1 to 3

• From -2 to 1

In the second example, what is the interval where the function is decreasing?

• From -infinity to -1 and from 1 to infinity

• From -1 to 1

• From 1 to 4

• From -3 to 1

In the second example, what is the interval where the function is increasing?

• From -1 to 1

• From 1 to infinity

• From -3 to 1

• From -infinity to -1

In the third example, what is the interval where the function is decreasing?

• From -3 to 1

• From 1 to 4

• From -infinity to -3

• From 4 to infinity

In the third example, what is the interval where the function is constant?

• From -infinity to -3

• From 1 to 4

• From -3 to 1

• From 4 to infinity

What common mistake should be avoided when identifying intervals?

• Reading the graph from right to left

• Using hard brackets instead of soft brackets

• Using the y-value instead of the x-value

• Ignoring the slope of the curve

What should you always use to join intervals?

• A comma

• A semicolon

• A union symbol

• A plus sign