Relations, Functions, & Linear vs. Nonlinear

Front

What is the plane containing the x-axis and the y-axis called?

Back

The coordinate plane.

Front

What is a function?

Back

A relation where each input (x-value) has exactly one output (y-value).

Front

How can you determine if a relation is a function?

Back

Check if each x-value has only one corresponding y-value.

Front

What is the difference between linear and nonlinear functions?

Back

Linear functions create straight lines when graphed, while nonlinear functions create curves.

Front

What is an example of a linear function?

Back

y = 2x + 3.

Front

What is an example of a nonlinear function?

Back

y = x^2.

Front

What does it mean for a function to be linear?

Back

It means the graph of the function is a straight line.

Front

What does it mean for a function to be nonlinear?

Back

It means the graph of the function is not a straight line and can be curved.

Front

Can a function have the same y-value for different x-values?

Back

Yes, as long as each x-value has only one y-value.

Front

Is the relation {(1,2), (1,3), (2,4)} a function?

Back

No, because the x-value 1 has two y-values (2 and 3).