Exploring Equations as Functions in Algebra

This video tutorial explores functions represented as equations, focusing on determining the domain and range. It explains the concept of functions as machines that take an input (x) and produce an output (y). The video provides several examples of linear functions, demonstrating how to calculate the range for given domains. The tutorial emphasizes the importance of listing domain and range values in order from least to greatest.

What is the primary objective of this video?

• To solve quadratic equations

• To learn about graphing linear equations

• To determine the domain and range of functions presented as equations

• To understand the concept of limits

What does the graph of an equation represent?

• The set of all possible x values

• The set of all possible y values

• The set of all ordered pairs

• The set of all constants

In a function, what is the independent variable?

• The constant term

• The input value

• The variable that depends on the output

• The output value

What is the dependent variable in a function?

• The input value

• The variable that is chosen independently

• The output value

• The constant term

Given the function y = x - 5, what is the range if the domain is {4, 6, 8}?

• {-1, 0, 3}

• {-2, 0, 3}

• {-1, 1, 2}

• {-1, 1, 3}

For the function y = 3x + 1, what is the range if the domain is {-1, 0, 1, 4}?

• {-2, 0, 3, 13}

• {-3, 0, 3, 12}

• {-2, 1, 4, 13}

• {-1, 1, 4, 12}

What is the range for the function y = 4 - x if the domain is {-2, 3, 5}?

• {-1, 1, 5}

• {-2, 1, 5}

• {-1, 2, 6}

• {-1, 1, 6}

For the function y = 3/5x + 2, what is the range if the domain is {-10, 0, 5}?

• {-3, 2, 4}

• {-3, 1, 4}

• {-4, 1, 3}

• {-4, 2, 3}

What is the range for the function y = 7 - 1/2x if the domain is {-4, 0, 6}?

• {3, 7, 8}

• {4, 6, 9}

• {4, 7, 9}

• {3, 6, 8}

For the function y = -2/3x + 9, what is the range if the domain is {-12, -6, 3}?

• {7, 12, 17}

• {6, 12, 16}

• {7, 13, 17}

• {6, 13, 16}