1. Linear Functions
January 11, 2017

2. Outline Essential Questions Vocabulary review
Identifying a linear function by a graph
Identifying a linear function by ordered pairs
Examples
Graphing linear functions
Outline

3. How do I identify a linear function from a graph and from ordered pairs?
How do I graph a linear function?
Essential Questions

4. Identifying a linear function by a graph
Types of graphs
Linear function
Not a linear function
Not a function
Identifying a linear function by a graph

5. Identifying a linear function by a graph
Straight line
Passes vertical line test

6. Identifying a linear function by a graph
Not a linear function
Identifying a linear function by a graph
Not a straight line
Passes vertical line test

7. Identifying a linear function by a graph
Not a function
Identifying a linear function by a graph
Not a straight line
Fails vertical line test

8. Identifying a linear function by a graph
Not a function
Identifying a linear function by a graph
A straight line
Fails vertical line test

9. Identifying a linear function by using ordered pairs
Types
Linear function
Not a linear function
Identifying a linear function by using ordered pairs

10. Identifying a linear function by using ordered pairs
Types
Linear function
Not a linear function
Identifying a linear function by using ordered pairs

11. Identifying a linear function by using ordered pairs
Constant rate of change in x values and y-values
No repeating y-values
Identifying a linear function by using ordered pairs

12. Identifying a linear function by using ordered pairs
YES
Identifying a linear function by using ordered pairs x y -2 7 -1 4 1 2 -5 -3 +1 -3 +1 +1 -3 +1 -3

13. Identifying a linear function by using ordered pairsNO
Identifying a linear function by using ordered pairs x y -2 6 -1 3 2 1

14. Identifying a linear function by using ordered pairsNO
Linear function
{(-10,10), (-5,4), (0,2), (5,0)}
Identifying a linear function by using ordered pairs x y
-10 10 -5 4 2 5 -6 +5 -2 +5 +5 -2

15. YES Linear function Examples {(0,-3), (4,0), (8,3), (12,6), (16,9)} x-3 4 8 3 12 6 16 9

16. NO
Linear function
Examples

17. NO
Linear function
Examples

18. NO Linear function Examples {(-4,13), (-2,1), (0,-3), (2,1), (4,13)} xy -4 13 -2 1 -3 2 4

19. YES
Linear function
Examples

20. Graphing linear functions
Make sure equation is in slope- intercept form.
Plug in x-value
Solve for y-value or f(x)
After completing chart, graph function.
Graphing linear functions

21. Graphing linear functions
f(x) = -3x+4
Graphing linear functions x -2 2 3 4
f(x) 10 -5 -8
f(x) = -3(-2)+4
=6+4
=10
f(x) = -3(2)+4
=-6+4
=-2
f(x) = -3(4)+4
=-12+4
=-8
f(x) = -3(0)+4
=0+4 =4
f(x) = -3(3)+4
=-9+4
=-5

22. Graphing linear functions
f(x) = -3x+4
Graphing linear functions x -2 2 3 4
f(x) 10 -5 -8

23. Graphing linear functions
f(x) = x+7
Graphing linear functions x -5 -4 -2 1
f(x) 2 3 5 7 8
f(x) = (-5)+7
=-5+7 =2
f(x) = (-2)+7
=-2+7 =5
f(x) = (1)+7
=1+7 =8
f(x) = (-4)+7
=-4+7 =3
f(x) = (0)+7
=0+7 =7

24. Graphing linear functions
f(x) = x+7
Graphing linear functions x -5 -4 -2 1
f(x) 2 3 5 7 8

25. Graphing linear functions
f(x) = 5x
Graphing linear functions x -5 -3 3 5
f(x)
-25
-15 15 25
f(x) = 5(-5)
=-25
f(x) = 5(0) =0
f(x) = 5(5)
=25
f(x) = 5(-3)
=-15
f(x) = 5(3)
=15

26. Graphing linear functions
f(x) = 5x
Graphing linear functions x -5 -3 3 5
f(x)
-25
-15 15 25