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 graph can be curved or have varying slopes.

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 constant, the function is linear.

Front

What is the slope of a linear function?

Back

The slope of a linear function is the ratio of the change in y to the change in x (rise over run). It indicates how steep the line is.

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 = 2x + 3, y = x^2, y = 1/x?

Back

y = 2x + 3 is a linear function.

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 is nonlinear?

Back

A graph is nonlinear if it curves or has bends, indicating that the rate of change is not constant.

Front

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

Back

A linear graph is a straight line, while a nonlinear graph can be curved or have varying slopes.

Front

What is an example of a nonlinear function?

Back

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