Linear and Nonlinear Functions Identifying functions on tables, graphs, and equations. Irma Crespo...
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Transcript of Linear and Nonlinear Functions Identifying functions on tables, graphs, and equations. Irma Crespo...
Linear and Nonlinear Functions
Identifying functions
on tables, graphs, and equations.
Irma Crespo 2010
Warm Up
Graph y = 2x + 1
Rewrite the linear equation 3y + x = 9 to its slope-intercept form or the “y = ” form.
What is the linear equation for this graph?
Compare and Contrast
Yards to Feet
Num
ber
of F
eet
Number of Yards
Yards to Square Yards
Length of a Side of a Square Yard
Are
a of
Squ
are
(yd2 )
Tables: Linear or Nonlinear
linear
nonlinear
x y
2 50
4 35
6 20
8 5
x y
1 1
4 16
7 49
10 100
Is the rate of change constant (the same)?
+2
+2
+2
-15
-15
-15
+3
+3
+3
+15
+33
+51
Identify: Linear or Nonlinear Table?
x y
0 20
5 16
10 12
15 8
x 0 2 4 6
y 0 2 8 18
linear
nonlinear
Graphs: Linear or Nonlinear
Is the graph a straight line?
linear linear nonlinear
Identify: Linear or Nonlinear Graph?
linear linear nonlinear
Equations: Linear or Nonlinear
REMEMBER: x1 = x and x0 = 1
In “y = ” form, is x raised to a power of 1 or 0?
Does x appear in the numerator?
y = x + 4y = 6/x
y = 4y = x3 + 1
y = ½ xlinear
nonlinear
linear
nonlinear
linear
Identify:Linear or Nonlinear Equation?
y = 2/x + 5y = x2 + 8y = .6x1 y = + 13x2
linear linearnonlinear nonlinear
Pointers to Keep in Mind
A graph is linear if it is a straight line.
A table is linear if the rate of change is constant.
There is a common difference.
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.
1. Table A
2. Graph
3. Equation x 3 6 9 12
y 12 10 8 6
a b c
y = + 58x
Complete the practice worksheet.
Work with a partner or on your own.
Submit completed worksheet for grading.
Solutions are discussed the next day.
Practice Worksheet
Main Resources
Day, et.al. (2009). Math Connects: Concepts, Skills, and Problem Solving. Chapter 10. Columbus:McGraw-Hill.
PowerPoint created by Irma Crespo. University of Michigan-Dearborn, School of
Education. Winter 2010.