Linear and Nonlinear Functions Identifying functions on tables

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

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

Compare and Contrast Yards to Square Yards Number of Feet Area of Square (yd 2) Yards to Feet Number of Yards Length of a Side of a Square Yard

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

Identify: Linear or Nonlinear Table? x y 0 20 5 16 10 12 15 8 w linear x 0 2 4 6 y 0 2 8 18 w nonlinear

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

Identify: Linear or Nonlinear Graph? w linear w nonlinear

Equations: Linear or Nonlinear w REMEMBER: x 1 = x and x 0 = 1 w In “y = ” form, is x raised to a power of 1 or 0? w Does x appear in the numerator? y=x+4 linear y = 6/x nonlinear y = x 3 + 1 y=½x linear nonlinear y=4 linear

Identify: Linear or Nonlinear Equation? y =. 6 x 1 y = x 2 + 8 y = 3 x 2 +1 y = 2/x + 5 linear nonlinear

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

Exit Slip w Identify if linear or nonlinear. 1. Tabl xe A 3 y 12 2. Grap ha 6 10 9 8 b 12 6 c 3. Equatio n y = x 8 + 5

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 l Day, et. al. (2009). Math Connects: Concepts, Skills, and Problem Solving. Chapter 10. Columbus: Mc. Graw-Hill. l Power. Point created by Irma Crespo. University of Michigan-Dearborn, School of Education. Winter 2010.