Parametric Functions Concepts

Mr. Bean introduces AP precalculus students to parametric functions, explaining their basic structure and how they differ from rectangular equations. The lesson covers creating tables, graphing parametric functions, and understanding graph direction and domain restrictions. An example with a restricted domain is provided to illustrate these concepts.

What is the main topic of today's lesson?

• Quadratic functions

• Parametric functions

• Linear equations

• Rectangular equations

What is a common dependent variable in rectangular equations?

• X

• Y

• Z

• T

In parametric functions, what is the independent variable often called?

• T

• Z

• X

• Y

What is the form of a parametric function?

• F(z) = (x(z), y(z))

• F(y) = x

• F(t) = (x(t), y(t))

• F(x) = y

What do you need to do to find the coordinate point in a parametric function?

• Solve for X and Y

• Plug in the parameter value

• Differentiate the function

• Graph the function

What is the first step in filling a table for parametric functions?

• Solve for Y

• Plug in T values

• Find the derivative

• Graph the function

When graphing parametric functions, what is important to start with?

• The midpoint of T

• The highest value of T

• Any random value of T

• The lowest value of T

What does the direction of a parametric graph indicate?

• The starting and ending points

• The slope of the graph

• The speed of the graph

• The order of points

What happens to a parametric graph with no restriction on the domain?

• It loops back to the start

• It forms a closed shape

• It stops at a certain point

• It extends indefinitely

What is a restricted domain in parametric functions?

• A domain that repeats

• A domain with a start and end point

• A domain with no limits

• A domain that is undefined