Evaluating Piecewise Functions

The video tutorial introduces piecewise functions, explaining that they are functions defined by multiple sub-functions, each with its own domain. It covers how to graph these functions using inequalities and demonstrates evaluating them at specific points. The tutorial also explores non-linear piecewise functions and the use of compound inequalities. Practical examples and graphing techniques using Desmos are provided to enhance understanding.

What is a piecewise function?

• A function that cannot be graphed.

• A function that is defined piece by piece.

• A function that only has linear parts.

• A function defined by a single equation.

Which of the following is an example of a piecewise graph?

• A graph with multiple disconnected parts.

• A graph with a single straight line.

• A graph with no gaps.

• A graph with a single curve.

In piecewise function notation, what does each 'case' represent?

• A different function for a specific interval.

• A constant value.

• A single function for all values of x.

• A point on the graph.

How do you restrict the domain of a function in Desmos?

• Using angle brackets.

• Using square brackets.

• Using curly braces.

• Using parentheses.

What is the value of f(0) for the piecewise function defined as 2x + 3 for x ≤ 2 and x - 4 for x > 2?

• 4

• 0

• 3

• 2

Which part of the piecewise function do you use to evaluate f(10) if the function is defined as 2x + 3 for x ≤ 2 and x - 4 for x > 2?

• Neither part

• Both parts

• x - 4

• 2x + 3

What type of function is used in the first case of the piecewise function with quadratic and linear parts?

• Linear

• Cubic

• Absolute value

• Quadratic

How do you handle strict inequalities in Desmos when graphing piecewise functions?

• Use parentheses.

• Use square brackets.

• Use curly braces.

• Use angle brackets.

What is a compound inequality in the context of piecewise functions?

• An inequality with only one bound.

• An inequality with no bounds.

• An inequality with both upper and lower bounds.

• An inequality that cannot be graphed.

What is the value of h(2) for the piecewise function defined as |x| + 3 for x < 0, x^3 + 3 for 0 ≤ x < 2, and -x + 2 for x ≥ 2?

• 0

• 4

• 3

• 2