Functions - Flashcard Review

Front

What is a linear relationship?

Back

A linear relationship is a relationship between two variables that can be represented by a straight line on a graph, indicating a constant rate of change.

Front

What is a function?

Back

A function is a relation where each input (x-value) has exactly one output (y-value).

Front

What does it mean if a relation is not a function?

Back

A relation is not a function if at least one input has two different outputs.

Front

How can you determine if a graph represents a linear function?

Back

A graph represents a linear function if it forms a straight line.

Front

What is the definition of a constant rate of change?

Back

A constant rate of change means that for every unit increase in the input, the output increases by a fixed amount.

Front

What does it mean for a function to be increasing?

Back

A function is increasing if, as the input values increase, the output values also increase.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed, indicating that the rate of change is not constant.

Front

What is the significance of the slope in a linear function?

Back

The slope indicates the rate of change of the function; a positive slope means the function is increasing, while a negative slope means it is decreasing.

Front

What does it mean for a function to be always increasing?

Back

A function is always increasing if its output values rise as the input values increase, without any decreases.

Front

What is the difference between a function and a relation?

Back

A function is a specific type of relation where each input has only one output, while a relation can have multiple outputs for a single input.