Linear and Nonlinear Functions

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Presentation transcript:

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

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

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

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