Linear vs Nonlinear Functions

Front

What is the definition of a function?

Back

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

Front

What distinguishes a linear function from a nonlinear function?

Back

A linear function has a constant rate of change and can be represented by a straight line on a graph, while a nonlinear function does not have a constant rate of change and can be represented by a curve.

Front

What is the general form of a linear function?

Back

The general form of a linear function is y = mx + b, where m is the slope and b is the y-intercept.

Front

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

Back

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

Front

How can you determine if a relation is a function using a table of values?

Back

A relation is a function if each input value (x) corresponds to exactly one output value (y). If any input value has multiple output values, it is not a function.

Front

What is the slope of a linear function?

Back

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

Front

What is a nonlinear function?

Back

A nonlinear function is a function that does not create a straight line when graphed, meaning it has a variable rate of change.

Front

How can you identify a linear function from its graph?

Back

A linear function can be identified by a straight line on the graph, while a nonlinear function will show a curve or bend.

Front

What is the significance of the y-intercept in a linear function?

Back

The y-intercept is the point where the line crosses the y-axis, representing the output value when the input value (x) is zero.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola.