Linear and Nonlinear Functions Identifying functions on tables, graphs, and equations. Irma Crespo 2010

Warm Up What is the linear equation for this graph? Graph y = 2x + 1 Rewrite the linear equation 3y + x = 9 to its slope-intercept form or the “y = ” form.

Length of a Side of a Square Yard Compare and Contrast Yards to Feet Number of Feet Number of Yards Yards to Square Yards Length of a Side of a Square Yard Area of Square (yd2)

Tables: Linear or Nonlinear Is the rate of change constant (the same)? x y 2 50 4 35 6 20 8 5 x y 1 4 16 7 49 10 100 +3 +15 +2 -15 +2 -15 +3 +33 +2 +3 +51 -15 linear nonlinear

Identify: Linear or Nonlinear Table? x y 20 5 16 10 12 15 8 x 2 4 6 y 8 18 nonlinear linear

Graphs: Linear or Nonlinear Is the graph a straight line? linear nonlinear linear

Identify: Linear or Nonlinear Graph?

Equations: Linear or Nonlinear REMEMBER: x1 = x and x0 = 1 In “y = ” form, is x raised to a power of 1 or 0? Does x appear in the numerator? y = 6/x y = x3 + 1 y = x + 4 nonlinear y = ½ x nonlinear y = 4 linear linear linear

Identify:Linear or Nonlinear Equation? 3x 2 y = .6x1 y = x2 + 8 y = 2/x + 5 linear nonlinear linear nonlinear

Pointers to Keep in Mind A table is linear if the rate of change is constant. There is a common difference. A graph is linear if it is a straight line. An equation is linear if the power of x is either 1 or 0 and it appears in the numerator.

Exit Slip Identify if linear or nonlinear. Table A Equation y = + 5 3 6 9 12 y 10 8 y = + 5 8 x Graph a b c

Practice Worksheet Complete the practice worksheet. Work with a partner or on your own. Submit completed worksheet for grading. Solutions are discussed the next day.

Main Resources Day, et.al. (2009). Math Connects: Concepts, Skills, and Problem Solving. Chapter 10. Columbus:McGraw-Hill. PowerPoint created by Irma Crespo. University of Michigan-Dearborn, School of Education. Winter 2010.