Evaluating and Graphing Piecewise Functions

This video tutorial covers the evaluation and graphing of piecewise functions. It begins with an introduction to piecewise functions, followed by examples of evaluating them. The tutorial then focuses on graphing techniques, including using a calculator for linear and non-linear functions. Advanced graphing techniques, such as handling absolute values and three-piece functions, are also discussed. Finally, the video explains how to write piecewise functions from given graphs.

What is a piecewise function?

• A function that is continuous everywhere

• A function that is split into multiple parts

• A function that has no domain

• A function that is always linear

What is the domain of the top piece of the function if the input is less than -1?

• X is less than -1

• X is greater than or equal to -1

• X is greater than -1

• X is equal to -1

If f(x) = x^2 - 5 for x < -1, what is f(-3)?

• 4

• 14

• 23

• 9

What is the output of the function f(x) = 2x + 9 for x = 7?

• 25

• 16

• 23

• 14

What does an open circle on a graph indicate?

• The function has a maximum at that point

• The function is undefined at that point

• The function is continuous at that point

• The function has a minimum at that point

When graphing piecewise functions, what tool is recommended for accuracy?

• A ruler

• A protractor

• Graph paper

• A compass

What shape does the graph of an absolute value function typically take?

• A V shape

• A parabola

• A straight line

• A circle

What is the slope of the line y = 5?

• 1

• 5

• Undefined

• 0

How do you determine the y-intercept of a line if it doesn't directly hit the y-axis?

• By measuring the slope

• By guessing

• By using a calculator

• By extending the line

What is the domain of the piecewise function if the piece starts at x = -2 and goes to the left?

• X = -2

• X < -2

• X >= -2

• X > -2