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

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

3. 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

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

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

6. Identify: Linear or Nonlinear Graph?

7. 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

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

9. 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.

10. Exit Slip Identify if linear or nonlinear. Table A Equation y = + 53 6 9 12 y 10 8
y = 8 x
Graph a b c

11. 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)