Graphing Piecewise Functions and Points

The video tutorial explains how to graph a piecewise defined function with three constant function rules. Each rule is graphed as a horizontal line segment based on specified intervals for x. The tutorial demonstrates the process of identifying the correct segment for each function rule and marking open or closed points at interval boundaries. The approach is useful for more complex functions.

What is a piecewise defined function?

• A function that is always decreasing

• A function with a single rule for all x values

• A function with multiple rules for different intervals of x

• A function that is always increasing

How many pieces does the graph of the given piecewise function have?

• One

• Two

• Four

• Three

For the function rule F(x) = -2, what type of point is used at x = -3?

• Both open and closed points

• Open point

• Closed point

• No point

What is the y-value of the horizontal line for the function rule F(x) = -2?

• 0

• -2

• -3

• 2

For the function rule F(x) = 1, what type of point is used at x = -3?

• Both open and closed points

• No point

• Closed point

• Open point

What type of point is used at x = 1 for the function rule F(x) = 1?

• Closed point

• No point

• Open point

• Both open and closed points

For the function rule F(x) = 4, what type of point is used at x = 1?

• No point

• Both open and closed points

• Closed point

• Open point

What is the y-value of the horizontal line for the function rule F(x) = 4?

• 2

• 1

• 3

• 4

What is the purpose of using open and closed points in graphing piecewise functions?

• To show where the graph is increasing

• To specify whether endpoints are included in the interval

• To indicate the start of a graph

• To make the graph look more complex

Why is it beneficial to graph the entire horizontal line before determining the piece needed?

• It saves time

• It is required by graphing rules

• It helps in visualizing the entire function

• It makes the graph look complete