Interval Notation for Function Behavior

The video tutorial explains how to identify increasing, decreasing, and constant intervals on a graph by focusing on X values rather than Y values. It emphasizes the importance of using open intervals and avoiding common mistakes, such as confusing Y values with X values. The tutorial includes examples to illustrate these concepts and provides additional resources for further learning.

What is the first step in identifying increasing intervals on a graph?

• Identify the endpoints

• Scan the graph from left to right

• Look at the Y values

• Check for constant intervals

When identifying increasing intervals, which values are we primarily interested in?

• X values

• Z values

• Slope values

• Y values

Why should increasing and decreasing intervals be represented as open intervals?

• To avoid confusion with constant intervals

• To simplify the notation

• To exclude the endpoints where the graph changes direction

• To include the endpoints

What symbol is used to represent open intervals?

• Square brackets

• Curly braces

• Angle brackets

• Parentheses

What is the interval notation for a graph that is increasing from X = 1 to positive infinity?

• [1, ∞)

• (1, ∞]

• [1, ∞]

• (1, ∞)

What does a constant interval on a graph look like?

• A vertical line

• A diagonal line

• A curved line

• A horizontal line

In the given example, what is the interval where the graph is constant?

• From X = -2 to X = 1

• From X = 0 to X = 3

• From X = -1 to X = 2

• From X = -3 to X = 1

What common mistake do students make when identifying decreasing intervals?

• Including the endpoints

• Using Y values instead of X values

• Using square brackets

• Ignoring constant intervals

What is the correct interval notation for a graph decreasing from X = -2 to X = 1?

• [-2, 1)

• (-2, 1]

• [-2, 1]

• (-2, 1)

When should you write a constant interval?

• When the graph is vertical

• When the graph is curved

• When the graph is diagonal

• When the graph is horizontal