Linear vs. Nonlinear

Front

What is a linear function?

Back

A linear function is a function that graphs to a straight line. It can be expressed in 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 graph to a straight line. Its graph can be curved or have a more complex shape.

Front

How can you identify a linear function from its graph?

Back

A linear function can be identified by its straight line graph, which has a constant slope.

Front

How can you identify a nonlinear function from its graph?

Back

A nonlinear function can be identified by its curved graph or any graph that does not form a straight line.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the rate of change of the function, represented by 'm' in the equation y = mx + b.

Front

What does the y-intercept represent in a linear function?

Back

The y-intercept is the point where the graph of the function crosses the y-axis, represented by 'b' in the equation y = mx + b.

Front

Can a linear function have a negative slope?

Back

Yes, a linear function can have a negative slope, which means the line decreases as it moves from left to right.

Front

Can a nonlinear function have a positive slope?

Back

Yes, a nonlinear function can have sections where it has a positive slope, but overall it does not form a straight line.

Front

What is an example of a linear function?

Back

An example of a linear function is f(x) = 2x + 3, which graphs to a straight line.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is f(x) = x^2, which graphs to a parabola.