Linear and Nonlinear Functions Identifying functions on tables

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

Warm Up w Graph y = 2 x + 1 w What is the linear equation for this graph?

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 An equation is linear if the x value is found in the numerator and if it has an exponent of 1 or 0. w If the x value is in the denominator or if it has any other exponent, it is nonlinear 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

Discrete vs. Continuous w A function is discrete if the graph has space between possible data (graph will be represented by dots) w A function is continuous if the graph has no space between data values (graph will be a solid line)