Graphing Piecewise-Defined Functions

This video tutorial teaches how to graph piecewise-defined functions by graphing each function and restricting the domain. It covers graphing horizontal lines, inequalities, step functions, and complex piecewise functions. The tutorial also explains how to evaluate piecewise functions for specific x values, understand their domain and range, and address common misunderstandings. Additionally, it demonstrates how to express the absolute value function as a piecewise function.

What is the equation of a horizontal line that crosses the y-axis at 2?

• x = y + 2

• y = x + 2

• x = 2

• y = 2

When graphing inequalities, what symbol is used to indicate that a number is not included in the inequality?

• Triangle

• Square

• Open circle

• Closed circle

What is a step function composed of?

• Vertical lines

• Horizontal lines

• Diagonal lines

• Curved lines

How do you represent the domain restriction for the function f(x) = x - 1, where 0 < x < 1?

• Using a dashed line

• Using open circles at x = 0 and x = 1

• Using closed circles at x = 0 and x = 1

• Using a solid line

What is the range of the function f(x) = x - 1 for 0 < x < 1?

• y is greater than 1

• y is greater than 0

• y is less than 0

• y is between -1 and 0

What is a common mistake when evaluating a piecewise-defined function at a specific point?

• Using only one piece of the function

• Using the wrong function type

• Ignoring the domain restrictions

• Substituting the value into both pieces of the function

How can the absolute value function be expressed as a piecewise function?

• f(x) = x for x < 0 and f(x) = -x for x >= 0

• f(x) = -x for x >= 0 and f(x) = x for x < 0

• f(x) = -x for x < 0 and f(x) = x for x >= 0

• f(x) = x for x >= 0 and f(x) = -x for x < 0