Relations and Functions

Front

What is a function?

Back

A function is a relation that assigns exactly one output value for each input value.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions have a constant rate of change and graph as straight lines, while nonlinear functions do not have a constant rate of change and can graph as curves.

Front

What is the definition of the domain of a function?

Back

The domain of a function is the set of all possible input values (x-values) that the function can accept.

Front

What is the definition of the range of a function?

Back

The range of a function is the set of all possible output values (y-values) that the function can produce.

Front

How can you determine if a relation is a function?

Back

A relation is a function if each input value corresponds to exactly one output value.

Front

What does it mean for a function to have a constant rate of change?

Back

A function has a constant rate of change if the difference in output values divided by the difference in input values is the same for any two points on the function.

Front

What is a linear function?

Back

A linear function is a function that can be expressed in the form y = mx + b, where m is the slope and b is the y-intercept.

Front

What is a nonlinear function?

Back

A nonlinear function is a function that cannot be written in the form y = mx + b and may include curves, parabolas, or other shapes.

Front

What is the slope of a line?

Back

The slope of a line is a measure of its steepness, calculated as the rise (change in y) over the run (change in x).

Front

What is a y-intercept?

Back

The y-intercept is the point where a line crosses the y-axis, represented as (0, b) in the equation y = mx + b.