Understanding Functions and Rates

This video introduces the concept of functions, explaining that a function assigns exactly one output for each input. It uses the analogy of function machines to illustrate how inputs are transformed into outputs through specific rules. Various methods of representing functions, such as tables, graphs, and ordered pairs, are discussed. The video also covers how to identify function rules and calculate unit rates using functions. The chapter concludes with a preview of upcoming topics in the series.

What is a function in mathematical terms?

• A process that assigns multiple outputs to a single input

• A process that assigns one input to multiple outputs

• A process that assigns exactly one output for each input

• A process that assigns no output to any input

In the 4X function machine, if the input is 3, what is the output?

• 7

• 8

• 12

• 15

What happens to the output in a function machine when the input changes?

• The output becomes negative

• The output changes as the input changes

• The output remains the same

• The output becomes zero

If the input is 2 and the output is 10 in a 5X function machine, what is the rule?

• Add 5

• Divide by 5

• Multiply by 5

• Subtract 5

What is the output if the input is 3 in a 5X function machine?

• 20

• 25

• 15

• 10

What is the algebraic expression for a function where the rule is to multiply by 5?

• y = x + 5

• y = x / 5

• y = 5x

• y = x - 5

Which of the following is NOT a way to represent a function?

• Paragraph

• Mapping diagram

• Graph

• Table

In a graph, which axis is typically used for the input values?

• Vertical axis

• Circular axis

• Horizontal axis

• Diagonal axis

What is the unit rate if 4 apples cost 3 dollars?

• 1 dollar per apple

• 2 dollars per apple

• 0.75 dollars per apple

• 1.5 dollars per apple

How do you determine if a relationship is a function?

• Check if there are no input values

• Check if each input value matches one output value

• Check if each output value matches multiple input values

• Check if each input value matches multiple output values