Graphing Piecewise Functions with Tables

Miss Burk introduces a video tutorial focusing on graphing piecewise functions, a topic students often struggle with. The video begins with a review of graphing inequalities, explaining concepts like open and closed circles. It then transitions to graphing piecewise functions using tables, emphasizing the importance of identifying function breakpoints. The tutorial covers both simple and complex piecewise functions, providing step-by-step guidance on plotting them accurately. The video aims to prepare students for the upcoming school year by reinforcing these foundational graphing skills.

What type of circle is used to represent the inequality x ≤ 3?

• Solid circle

• Closed circle

• Open circle

• Dashed circle

For the inequality x > -4, why is an open circle used at -4?

• Because -4 is a boundary

• Because -4 is included

• Because -4 is a midpoint

• Because -4 is not included

In a compound inequality, what does the notation -2 < x ≤ 5 mean?

• x is less than or equal to -2 and greater than 5

• x is less than -2 and greater than 5

• x is greater than -2 and less than 5

• x is greater than -2 and less than or equal to 5

When graphing the piecewise function 3x + 8 for x < -2, what is the y-value when x = -3?

• 0

• 1

• 2

• -1

What shape does the graph of x^2 + 4 take?

• Line

• Parabola

• Hyperbola

• Circle

For the function x^2 + 4, what is the y-value when x = 0?

• 2

• 8

• 0

• 4

In the more complex piecewise function, what is the boundary point for the first piece?

• -2

• -1

• 0

• 2

For the piecewise function with three pieces, what is the y-value when x = -1 for the second piece?

• 1

• 2

• 0

• 3

What is the slope of the first piece of the more complex piecewise function?

• 4

• 1

• 2

• 3

What is the y-value when x = 3 for the third piece of the more complex piecewise function?

• 0

• 2

• 1

• -1