Exploring Functions and Relations in Algebra

This video tutorial covers the identification of functions, the use of the vertical line test, and the determination of domain and range. It explains how to identify independent and dependent variables in functions and provides examples to illustrate these concepts. The tutorial also demonstrates how to calculate the range from a given domain using a function.

What is a function in terms of input and output?

• A relation where each input has exactly one output

• A relation where each input has multiple outputs

• A relation where each output has multiple inputs

• A relation where inputs and outputs are the same

Why is the relation with input 4 going to both 0 and 3 not a function?

• Because it has more than one output for a single input

• Because it has no inputs

• Because it has no outputs

• Because it has more than one input

What does the vertical line test determine?

• If a graph represents a function

• If a graph has multiple outputs

• If a graph is a straight line

• If a graph has multiple inputs

What happens if a vertical line passes through more than one point on a graph?

• The graph represents a function

• The graph does not represent a function

• The graph has no inputs

• The graph is a straight line

What is the domain of a function?

• The set of all possible output values

• The set of all possible z-values

• The set of all possible input values

• The set of all possible y-values

How do you typically write the domain and range of a function?

• In random order

• In reverse numerical order

• In numerical order from least to greatest

• In alphabetical order

What is the independent variable in a function?

• The variable that represents the output values

• The variable that represents the input values

• The variable that depends on the output

• The variable that is always constant

In the equation y = -x + 10, which variable is dependent?

• x

• y

• Both x and y

• Neither x nor y

Given the domain {0, 1, 2, 3, 4}, what is the range for the function y = -3x + 12?

• {-12, -9, -6, -3, 0}

• {0, 1, 2, 3, 4}

• {12, 9, 6, 3, 0}

• {0, 3, 6, 9, 12}

How do you find the range of a function given its domain?

• By dividing the domain values

• By plugging the domain values into the function

• By subtracting the domain values

• By adding the domain values