Understanding Piecewise Functions

The video tutorial introduces piecewise functions, explaining their definition and how they consist of multiple equations, each with its own domain. It guides viewers through sketching the graph of a piecewise function by following the given domains and calculating specific function values. The tutorial also provides an example of solving a different piecewise function, demonstrating the process of finding function values and sketching the graph.

What is a piecewise function?

• A function with a single equation

• A function that has no domain

• A function that is always linear

• A function with multiple equations, each defined on a specific domain

In a piecewise function, what does each equation represent?

• A different range

• A different domain

• A different variable

• A different constant

When sketching the first part of a piecewise function, what should you consider?

• The color of the graph

• The range of the function

• The domain of the function

• The type of function

How do you represent a point that is included in the domain on a graph?

• With a triangle

• With a square

• With a closed circle

• With an open circle

What is the value of the function at x = -1 for the first part of the piecewise function?

• 3

• 2

• 1

• 0

How do you find the overall domain of a piecewise function?

• By finding the intersection of all domains

• By considering only the first part

• By combining the domains of all parts

• By looking at the range of each part

What is the value of f(0) for the given piecewise function?

• 3

• 1

• 0

• 2

Which equation would you use to find f(3) in the given piecewise function?

• x^3

• x - 1

• x^2

• x + 2

When solving a different piecewise function, what is the first step?

• Identifying the domains

• Sketching the graph

• Finding the range

• Calculating specific values

What is the value of f(-1) for the different piecewise function?

• 1

• 0

• 3

• 2