1. Transforming Linear Functions
Algebra

2. Transforming Linear Functions
Exploration, on your own graphing calculator, or on a TI-Nspire
Transforming Linear Functions

3. Transforming Linear Functions
Up three
Transforming Linear Functions

4. Transforming Linear Functions
Down two
Transforming Linear Functions

5. Transforming Linear Functions
Right three or
Down six
Transforming Linear Functions

6. Transforming Linear Functions
Left two or
Up four
Transforming Linear Functions

7. Transforming Linear Functions

8. Transforming Linear Functions
Graph the following
f1(x) = 2x + 3
f2(x) = -f1(x)
Reflected across the x-axis
Transforming Linear Functions

9. Transforming Linear Functions
Graph the following
f1(x) = 2x + 3
f2(x) = f1(-x)
Reflected across the y-axis
Transforming Linear Functions

10. Transforming Linear Functions
Graph the following
f1(x) = x+2
f2(x) = 3(x+2)
f3(x) = -2(x+2)
Stretched in y direction
Transforming Linear Functions

11. Transforming Linear Functions
Graph the following
f1(x) = x+2
f2(x) = 3(x+2)
f3(x) = -2(x+2)
Note how they all cross through y=0
Transforming Linear Functions

12. Transforming Linear Functions
Graph the following
f1(x) = x+2
f2(x) = x/3 +3
f3(x) = x/(-2) +3
Note how they all cross through x=0
Transforming Linear Functions

13. Transforming Linear Functions

14. Transforming Linear Functions

15. Transforming Linear Functions

16. Transforming Linear Functions

17. Transforming Linear Functions

18. Transforming Linear Functions

19. Transforming Linear Functions

20. Transforming Linear Functions

21. Transforming Linear Functions

22. Transforming Linear Functions

23. Transforming Linear Functions

24. Transforming Linear Functions

25. Transforming Linear Functions

26. Transforming Linear Functions - Practice
Let g(x) be the indicated transformation of f(x) = 2x – 3
Write the rule for g(x)
Horizontal translation 3 units right
g(x) = 2x – 9
Horizontal translation 5 units left
g(x) = 2x +7
Transforming Linear Functions - Practice

27. Transforming Linear Functions - Practice
Let g(x) be the indicated transformation of f(x) = 2x – 3
Write the rule for g(x)
Vertical translation 3 units up
g(x) = 2x
Vertical translation 5 units down
g(x) = 2x – 8
Transforming Linear Functions - Practice

28. Transforming Linear Functions - Practice
Let g(x) be the indicated transformation of f(x) = 2x – 3
Write the rule for g(x)
reflection across the x-axis
g(x) = –2x + 3
reflection across the y-axis
g(x) = – 2x – 3
Transforming Linear Functions - Practice

29. Transforming Linear Functions - Practice
Let g(x) be the indicated transformation of f(x) = 2x – 3
Write the rule for g(x)
vertical stretch by a factor of 3
g(x) = 6x – 9
vertical shrink by a factor of 1/2
g(x) = x – 1.5
Transforming Linear Functions - Practice

30. Transforming Linear Functions - Practice
Let g(x) be the indicated transformation of f(x) = 2x – 3
Write the rule for g(x)
horizontal stretch by a factor of 3
g(x) = 2x/3 – 3
horizontal shrink by a factor of 1/2
g(x) = 4x – 3
Transforming Linear Functions - Practice

31. Transforming Linear Functions - Practice
Let g(x) be the indicated transformation of f(x) = 2x – 3
Write the rule for g(x)
Vertical shift up by 5 followed by a
horizontal stretch by a factor of 2
g(x) = x + 2
horizontal shift left by 4 followed by a
reflection in the x-axis
g(x) = – 2x – 13
Transforming Linear Functions - Practice

32. Transforming Linear Functions - Practice
Let g(x) be the indicated transformation of f(x) = 2x – 3
Write the rule for g(x)
Vertical shift down by 7 followed by a
Vertical shrink by a factor of 2
g(x) = x – 5
horizontal shift right by 1 followed by a
reflection in the y-axis
g(x) = – 2x – 5
Transforming Linear Functions - Practice

33. Pages 138 – 140
8 – 14, 19, 35 – 38
Homework