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 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 take various forms such as quadratic, cubic, or exponential.

Front

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

Back

A linear function will have a constant rate of change between the x-values and y-values. If the differences in y-values divided by the differences in x-values are the same, the function is linear.

Front

What is the slope of a linear function?

Back

The slope of a linear function is a measure of how steep the line is. It is calculated as the change in y divided by the change in x (rise/run).

Front

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

Back

The y-intercept is the point where the line crosses the y-axis. It represents the value of y when x is 0.

Front

Which of the following equations represents a linear function: y=3x+2, y=x^2, y=5?

Back

y=3x+2 and y=5 represent linear functions. y=x^2 is nonlinear.

Front

What is the general form of a linear equation?

Back

The general form of a linear equation is Ax + By = C, where A, B, and C are constants.

Front

How can you tell if a graph represents a nonlinear function?

Back

A graph represents a nonlinear function if it curves or has bends, rather than being a straight line.

Front

What is the difference between a linear equation and a nonlinear equation?

Back

A linear equation has a constant rate of change and graphs as a straight line, while a nonlinear equation has a variable rate of change and graphs as a curve.

Front

What is an example of a nonlinear function?

Back

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