Graphing Piecewise Functions with Tables

This video tutorial introduces AP Calculus students to graphing piecewise functions using tables of values. It begins with a review of graphing inequalities on a number line, emphasizing the importance of open and closed circles. The instructor then demonstrates how to graph piecewise functions by creating tables of values for different function segments, highlighting common student mistakes. The video concludes with a detailed example involving a three-part piecewise function, using interval notation and graphing techniques to illustrate the process.

What does a closed circle on a number line represent when graphing inequalities?

• The value is a midpoint.

• The value is included in the solution set.

• The value is an approximation.

• The value is excluded from the solution set.

When graphing X is greater than negative 4, where do you place the open circle?

• On negative 3

• On negative 4

• On negative 2

• On negative 5

In a piecewise function, what does an open circle at a point indicate?

• The point is excluded from the function.

• The point is included in the function.

• The point is a minimum.

• The point is a maximum.

For the function 3x + 8 when X is less than negative 2, what is the value of f(X) when X is -3?

• 0

• 1

• -1

• 2

What is the value of f(X) for the function ax^2 + 4 when X is 0?

• 8

• 0

• 4

• 1

How do you graph the point (-2, 8) for the function ax^2 + 4?

• With a triangle

• With a closed circle

• With a square

• With an open circle

In interval notation, what does the notation (-∞, -1) indicate?

• X is between -1 and 1

• X is less than -1

• X is greater than -1

• X is equal to -1

For the function 2x when X is between -1 and 2, what is the value of f(X) when X is 1?

• 4

• 1

• 2

• 3

What is the value of f(X) for the function -X + 3 when X is 3?

• 3

• 2

• 1

• 0

When graphing a piecewise function, what does an arrow at the end of a line indicate?

• The function has a minimum value there.

• The function has a maximum value there.

• The function stops at that point.

• The function continues indefinitely in that direction.