Understanding Functions and Their Properties

This video tutorial explains how to graph a piecewise defined function with three function rules. It covers graphing constant functions as horizontal lines and linear functions as slanted lines. The tutorial demonstrates graphing F(x) = 4 for x < -3, F(x) = -X - 1 for -3 <= x < 1, and F(x) = -1 for 1 <= x < 3. Each section includes identifying intervals, plotting points, and erasing unnecessary parts of the graph. The video concludes with a summary of the graphing process.

What is a piecewise function?

• A function with a single rule

• A function defined by multiple sub-functions

• A function that is always constant

• A function that is always linear

Which of the following is a characteristic of a constant function?

• It has a slope of zero

• It passes through the origin

• It has a variable slope

• It is always increasing

For the function f(x) = 4, what type of line is graphed?

• Diagonal line

• Horizontal line

• Vertical line

• Curved line

What is the y-intercept of the function f(x) = -x - 1?

• 1

• 3

• 0

• -1

In the interval -3 <= x < 1, what type of point is used at x = -3?

• Open point

• Closed point

• Double point

• No point

For the function f(x) = -1, what is the y-coordinate of the line?

• -1

• 0

• 3

• 1

In the interval 1 <= x < 3, what type of point is used at x = 3?

• Open point

• Closed point

• No point

• Double point

Which piece of the piecewise function corresponds to the rule f(x) = 4?

• Red piece

• Yellow piece

• Green piece

• Blue piece

Which piece of the piecewise function corresponds to the rule f(x) = -x - 1?

• Blue piece

• Green piece

• Yellow piece

• Red piece

Which piece of the piecewise function corresponds to the rule f(x) = -1?

• Red piece

• Blue piece

• Green piece

• Yellow piece