Linear vs 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 a constant rate of change and 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 form a straight line when graphed. Its rate of change is not constant, and it can be represented by equations that include exponents, roots, or other non-linear terms.

Front

How can you identify a linear function from a table of values?

Back

A linear function will have a constant difference between the y-values for equal intervals of x-values. If the differences are not constant, the function is nonlinear.

Front

What does the graph of a linear function look like?

Back

The graph of a linear function is a straight line that can slope upwards, downwards, or be horizontal.

Front

What does the graph of a nonlinear function look like?

Back

The graph of a nonlinear function can take various shapes, such as curves, parabolas, or circles, and does not form a straight line.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of its steepness, calculated as the change in y divided by the change in x (rise over run).

Front

What is the y-intercept in a linear function?

Back

The y-intercept is the point where the graph of a linear function crosses the y-axis, represented by the value of 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 indicates that as x increases, y decreases.

Front

What is an example of a nonlinear function?

Back

An example of a nonlinear function is y = x^2, which represents a parabola.

Front

How can you determine if a function is linear or nonlinear from its equation?

Back

If the equation can be simplified to the form y = mx + b, it is linear. If it includes variables raised to powers other than one, it is nonlinear.