Understanding Function Rules and Graphs

The video tutorial explains how to graph a piecewise-defined function with three distinct rules. It covers the process of graphing horizontal lines for constant functions and linear functions in slope-intercept form. The tutorial demonstrates how to graph each piece of the function based on specified intervals, ensuring correct use of open and closed points. The video emphasizes understanding the structure of piecewise functions and provides step-by-step guidance for graphing each segment accurately.

What is the general form of a piecewise function?

• A quadratic equation

• A constant function

• A single linear equation

• Multiple equations defined over different intervals

For the function rule f(x) = 3, what type of line is represented?

• Curved line

• Horizontal line

• Vertical line

• Diagonal line

At which point does the first function rule f(x) = 3 end?

• x = -3

• x = -2

• x = 0

• x = 1

What is the slope of the line for the function rule f(x) = x + 1?

• 2

• -1

• 0

• 1

For the function rule f(x) = x + 1, what is the y-intercept?

• 2

• -1

• 1

• 0

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

• Closed point

• Open point

• No point

• Intersection point

For the function rule f(x) = 1, what type of line is represented?

• Curved line

• Horizontal line

• Diagonal line

• Vertical line

At which point does the third function rule f(x) = 1 start?

• x = 2

• x = -1

• x = 1

• x = 0

What is the significance of an open point in a piecewise function graph?

• It marks the end of the graph

• It shows the function is continuous

• It represents a maximum value

• It indicates the function is undefined at that point

What is the final step in graphing a piecewise function?

• Calculating the slope

• Finding the y-intercept

• Drawing all possible lines

• Erasing unnecessary parts of the lines