Linear and Nonlinear Functions

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, and it can take various forms such as quadratic, exponential, etc.

Front

What does it mean for a relation to be 'Not a Function'?

Back

A relation is 'not a function' if there are at least two ordered pairs with the same first element but different second elements, meaning it does not pass the vertical line test.

Front

Identify if the following is linear or nonlinear: y = 4x + 6

Back

Linear

Front

Identify if the following is linear or nonlinear: y = x^2 + 3

Back

Nonlinear

Front

What is the slope in the linear function y = 2x + 5?

Back

The slope is 2.

Front

What is the y-intercept in the linear function y = -3x + 4?

Back

The y-intercept is 4.

Front

How can you determine if a table of values represents a linear function?

Back

If the differences between consecutive y-values are constant for equal differences in x-values, it represents a linear function.

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 an example of a nonlinear function?

Back

An example of a nonlinear function is y = 3x^2 - 2.