Graphing Piecewise Functions: Techniques and Strategies

The video tutorial explains how to graph piecewise functions using two methods. The first method involves graphing linear, horizontal, and parabolic functions with domain restrictions, while the second method uses tables to plot points for graphing. The tutorial provides step-by-step instructions and examples to help students understand the process. The video aims to make learning math less stressful and encourages students to explore further resources for mastering piecewise functions.

What is the first step in graphing a piecewise function?

• Identify the y-intercept

• Plot the vertex

• Draw the x-axis

• Determine the domain restrictions

For the function y = 2x + 4, what is the y-intercept?

• -1

• 0

• 4

• 2

When graphing y = 2x + 4 for x ≤ -1, what type of line should be drawn at x = -1?

• No line

• Vertical line

• Dashed or dotted line

• Solid line

What type of line represents y = 3 in the piecewise function?

• Vertical line

• Diagonal line

• Horizontal line

• Curved line

For the function y = 3, what is the domain restriction?

• x < -1

• x > 2

• x = 3

• -1 < x < 2

What is the vertex of the parabola y = (x - 3)^2 + 2?

• (3, 2)

• (-3, -2)

• (2, 3)

• (0, 0)

For the function y = (x - 3)^2 + 2, what is the domain restriction?

• x > 3

• x < 2

• x ≥ 2

• x ≤ 2

In the second method, what is the dividing line for the piecewise function?

• x = 0

• x = -1

• x = 1

• x = 2

When using the table method, what value is used to represent an open circle?

• 1

• 0

• 2

• 3

For the function y = 3x - 3, what is the y-value when x = 2?

• 0

• 3

• 6

• -3