Intervals of Increasing and Decreasing in Functions

The video tutorial introduces the concept of absolute value and graph behavior, focusing on interval notation to describe increasing and decreasing intervals. It provides examples of interval notation and explains how to express graph behavior using this notation. The tutorial also covers the end behavior of graphs, including parabolas and square root graphs, and discusses how to interpret these behaviors in terms of x and y values.

What is the primary purpose of interval notation?

• To write inequalities in a different form

• To find the roots of a function

• To solve equations

• To describe the behavior of graphs

In interval notation, what symbol is used to indicate that an endpoint is included?

• Angle bracket

• Curly brace

• Bracket

• Parenthesis

How would you write the interval notation for x being between -4 and 2, not including 2?

• (-4, 2]

• [-4, 2]

• (-4, 2)

• [-4, 2)

What does the union symbol (U) represent in interval notation?

• Intersection of two intervals

• Combination of two intervals

• Difference of two intervals

• Symmetric difference of two intervals

When describing increasing and decreasing intervals, which coordinate is primarily considered?

• W-coordinate

• X-coordinate

• Z-coordinate

• Y-coordinate

In the context of graph behavior, what does it mean if a graph is 'increasing'?

• The y-values are decreasing as x-values increase

• The x-values are increasing as y-values decrease

• The y-values are increasing as x-values increase

• The x-values are decreasing as y-values increase

What is the end behavior of a graph?

• The behavior of the graph at its maximum point

• The behavior of the graph at the origin

• The behavior of the graph as x approaches positive or negative infinity

• The behavior of the graph at its minimum point

For a parabola facing upwards, what is the end behavior as x approaches negative infinity?

• f(x) approaches positive infinity

• f(x) remains constant

• f(x) approaches negative infinity

• f(x) approaches zero

What happens to the y-values of a square root graph as x approaches positive infinity?

• They remain constant

• They approach positive infinity

• They approach zero

• They approach negative infinity

If a graph has a negative sign in front of the absolute value function, what transformation occurs?

• The graph shifts to the right

• The graph shifts to the left

• The graph flips vertically

• The graph flips horizontally