Understanding Functions and Their Graphs

Front

What is a function?

Back

A function is a relation that assigns exactly one output for each input. In other words, for every x-value, there is one and only one corresponding y-value.

Front

What is the rate of change in a linear function?

Back

The rate of change in a linear function is the slope, which represents how much the output (y) changes for a unit change in the input (x).

Front

Back

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not have a constant rate of change, meaning its graph is not a straight line. Examples include quadratic functions, exponential functions, etc.

Front

What is the difference between a function and a relation?

Back

A relation is any set of ordered pairs, while a function is a specific type of relation where each input is associated with exactly one output.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if no two ordered pairs have the same first element (input) with different second elements (outputs).

Front

What is the slope-intercept form of a linear equation?

Back

Front

How do you determine if a relation is a function from a table of values?

Back

To determine if a relation is a function from a table, check if any x-value is repeated with different y-values. If it is, then it is not a function.

Front

What is the graph of a linear function?

Back

The graph of a linear function is a straight line that can either slope upwards, downwards, or be horizontal.

Front

What is an example of a quadratic function?

Back