Functions: Linear vs. Nonlinear

Front

What is a function?

Back

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

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line, showing a constant rate of change.

Front

What is a nonlinear function?

Back

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

Front

How can you tell if a set of coordinates is not a function?

Back

If any input (x-value) is paired with more than one output (y-value), it is not a function.

Front

What does it mean for a relation to be a function?

Back

A relation is a function if each input is associated with exactly one output.

Front

What is an example of a linear function?

Back

y = 2x + 3 is a linear function.

Front

What is an example of a nonlinear function?

Back

y = x^2 is a nonlinear function.

Front

What is the slope of a linear function?

Back

The slope is the rate of change of the function, representing how much y changes for a change in x.

Front

What is a table of values?

Back

A table of values lists pairs of input (x) and output (y) values for a function.

Front

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

Back

If the differences between consecutive y-values divided by the differences in x-values are constant, it is linear.