Linear and Nonlinear Functions HOW DO YOU IDENTIFY

Linear and Nonlinear Functions HOW DO YOU IDENTIFY LINEAR FUNCTIONS ON TABLES, GRAPHS, AND EQUATIONS. Irma Crespo 2010

January 8, 2018 Warm-up 1. Two angles are linear pair. Their measures are represented by x + 10, and 3 x + 10. What are the measures of the angles? 2. Solve the equation. 2 + 3(x + 4) = 2(x + 7) We are TIGERS! Talented Intelligent Gifted Educated Resourceful Students Now watch me ROAR!

Review

Determine if the relation is a function. If it is not a function can you change some numbers so that it is a function? x 0 1 2 3 y 2 3

Determine if the relation is a function. If it is not a function can you change some numbers so that it is a function? x -1 1 y 1 2 3 4

Which of the following represent a function and why?

Which lines below are functions? Line a Line b Line c

Determine if the relation is a function. If it is not a function can you change it to be a function?

Determine if the relation is a function. If it is not a function can you change it to be a function?

Choose all the equations that are functions. Explain why you did not choose some equations. y = 12 x 2 + y 2 = 12 3 x + 4 y = 12 x = 12 y = 2 x + 12

Essential Questions How can I identify when a function is linear? How can I identify when a function is non-linear? How are linear functions useful?

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 linear -15 +3 x y 1 1 4 16 7 49 10 100 nonlinear +15 +33 +51

Identify: Linear or Nonlinear Table? x y 0 20 5 16 10 12 20 4 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 w In “y = mx + b ” form, is x raised to a power of 1 or 0? w Does x appear in the numerator? y=x+4 linear y = x 3 + 1 nonlinear y=4 linear

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

Pointers to Keep in Mind w 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. w An equation is linear if the power of x is understood as being 1 and it appears in the numerator.

Homework Study

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

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.