2/11 - Linear vs. Nonlinear

Front

What is a function?

Back

A function is a relation between a set of inputs and a set of possible outputs where each input is related to exactly one output.

Front

What is a linear function?

Back

A linear function is a function that can be graphically represented as a straight line. It has 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 does not form a straight line when graphed. Its rate of change is not constant.

Front

How can you determine if a table represents a function?

Back

A table represents a function if each input (x-value) corresponds to exactly one output (y-value). If any input has multiple outputs, 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 how steep the line is, calculated as the change in y divided by the change in x (rise/run).

Front

What does the y-intercept represent 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 is zero.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

What is the difference between a linear and a nonlinear graph?

Back

A linear graph is a straight line, indicating a constant rate of change, while a nonlinear graph is curved, indicating a variable rate of change.

Front

Can a function be both linear and nonlinear?

Back

No, a function cannot be both linear and nonlinear. It is either one or the other based on its graph and equation.

Front

What is an example of a nonlinear function?

Back

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