Linear vs. Nonlinear Models

Linear vs. Nonlinear Models

If the (simplified) ratio of change between any two points is the SAME, the function is LINEAR.

If the slope between any two points is NOT the same, it's NONLINEAR.

Multiple Choice

Which answer choice is true?

• The table represents a linear function because there is a pattern for the x-coordinates and y-coordinates.

• The table represents a linear function because the ratio of the change in the y value and the change in the x value is constant.

• The table represents a nonlinear function because the ratio of the change in the y value and the change in the x value is not constant.

• The table does not represent a function because there is more than one output for at least one input.

Multiple Choice

Which table(s) represent nonlinear functions?

• Table 1, only.
• Table 2, only
• Tables 1 and 3, only
• Tables 2 and 3, only

Multiple Choice

Select the linear equation.

Multiple Choice

Which equations represent linear functions?

• Equations 1 and 2, only

• Equations 1 and 4, only

• Equations 2 and 3, only

• Equations 1, 3, and 4, only

Multiple Select

Which equations describe a linear function? Select all that apply.

• x - 3y=12

• y=x³

• 3y=x

• y=5x²+6x

• 4x+3y²=24

Multiple Choice

Choose the function that is nonlinear.

• y = 2x³ - x² + 5

• y = 5x - 19

• 14x - 8 = 2y

• 3y = 6x + 15

Multiple Select

Which equations represent nonlinear functions? Select all that apply.

• y= 3x-4

• y=9x²+7x

• y=x

• y=2x³

• 2x²=y+4

Multiple Choice

Is this function linear or nonlinear?

• Linear function

• Nonlinear function

Multiple Select

Which show a linear function? Select 2.

Multiple Choice

Which of the function(s) above are linear?

• Function I, only

• Function II, only

• Function I and Function II, only

• Function I, Function II, and Function III

Multiple Choice

Which graph(s) show nonlinear functions?

• Graph I, only

• Graph II, only

• Graph I and Graph II, only.

• Graph I, Graph II, and Graph III

Multiple Choice

Which statement is true?

• Both Graphs have multiple y intercepts

• Both graphs are not functions

• The first graph is linear because it has a constant rate of change.

• The second graph is nonlinear but has a constant rate of change.