Identifying Functions

Front

What is the definition of a function?

Back

A function is a relation where every input has only ONE output.

Front

What does it mean for a function to be linear?

Back

A linear function is a function whose graph is a straight line, indicating a constant rate of change.

Front

What does it mean for a function to be nonlinear?

Back

A nonlinear function is a function whose graph is not a straight line, indicating a variable rate of change.

Front

Identify the characteristics of a linear function.

Back

Linear functions have a constant slope and can be represented by the equation y = mx + b.

Front

Identify the characteristics of a nonlinear function.

Back

Nonlinear functions can have curves, bends, or changes in direction and cannot be represented by a straight line.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x, often represented as 'm' in the equation y = mx + b.

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 changes in x-values, the function is linear.

Front

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

Back

If the differences between consecutive y-values are not constant for equal changes in x-values, the function is nonlinear.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2.