1. 4.7: Transformations of Linear Functions
Do Now
Determine the constant of variation to the following equations:
3x – y = 0
2) Suppose y varies directly as x, and y = 16 when x = 12. Find x when y = 20.
3) As you watch a movie, 24 individual pictures or frames flash a screen (s) each second. Create an equation y where s is screen.
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4.7: Transformations of Linear Functions

2. 4.7: Transformations of Linear Functions
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4.7: Transformations of Linear Functions

3. Transformations of Functions
Section 4.7
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4.7: Transformations of Linear Functions

4. 4.7: Transformations of Linear Functions
Equations
Slope Equation:
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4.7: Transformations of Linear Functions

5. 4.7: Transformations of Linear Functions
Recall
Slope
Y-intercept
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4.7: Transformations of Linear Functions

6. Transformations of Functions
The parent function equation of a linear function is y = x.
The equation of a line using Slope-Intercept form is y = mx + b where m is the slope and b is the y-intercept
The change is slope or m does change in size. The larger the m, the steeper it gets. The smaller the m, the flatter it gets. It does not matter whether the m is positive or negative.
The change of the y-intercept or b does not change in size. It changes in location.
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4.7: Transformations of Linear Functions

7. 4.7: Transformations of Linear Functions
Recall
Graph y = x
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4.7: Transformations of Linear Functions

8. 4.7: Transformations of Linear Functions
Example 1
Graph y = x + 3 and compare to y = x x
Process Column y –2 –1 1 2 1 2 3 4 5
The y-intercept shifts up 3 spots from the parent function
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4.7: Transformations of Linear Functions

9. 4.7: Transformations of Linear Functions
Example 2
Graph y = x – 4 and compare to y = x
The y-intercept shifts down 4 spots from the parent function
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4.7: Transformations of Linear Functions

10. 4.7: Transformations of Linear Functions
Example 3
Graph y = 2x and compare to y = x x
Process Column y –2 –1 1 2 –1 –2 2 4
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4.7: Transformations of Linear Functions

11. 4.7: Transformations of Linear Functions
Example 3
Graph y = 2x and compare to y = x
The slope of y = 2x is 2 times steeper than y = x
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4.7: Transformations of Linear Functions

12. 4.7: Transformations of Linear Functions
Example 4
Graph y = 1/2x and compare to y = x x
Process Column y –2 –1 1 2 –1
–1/2 1
The slope of y = 1/2x is 1/2 times flatter than y = x
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4.7: Transformations of Linear Functions

13. Graphing Calculator Ex 3 and 4
Graph y = 2x and compare to y = x
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4.7: Transformations of Linear Functions

14. 4.7: Transformations of Linear Functions
Example 5
Draw the function from the parent function y = x and the y-intercept moves up 4 spaces
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4.7: Transformations of Linear Functions

15. 4.7: Transformations of Linear Functions
Your Turn
Draw the function from the parent function y = x and the y-intercept moves down 5 spaces
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4.7: Transformations of Linear Functions

16. 4.7: Transformations of Linear Functions
Example 6
Draw the function from the parent function y = x and the slope is 2 times the original function
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4.7: Transformations of Linear Functions

17. 4.7: Transformations of Linear Functions
Example 7
Draw the function from the parent function y = x and the slope is 1/2 times the original function
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4.7: Transformations of Linear Functions

18. 4.7: Transformations of Linear Functions
Example 8
Draw the function from the parent function y = x and the slope is 1/3 times the original function, reflected
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4.7: Transformations of Linear Functions

19. 4.7: Transformations of Linear Functions
Your Turn
Draw the function from the parent function y = x and the slope is 4 times the original function
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4.7: Transformations of Linear Functions

20. 4.7: Transformations of Linear Functions
Example 9
Draw the function from the parent function y = x and the slope is 5 times the original function and moves down 2 up from the y-intercept
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4.7: Transformations of Linear Functions

21. 4.7: Transformations of Linear Functions
Example 10
Draw the function from the parent function y = x and the slope is 1/4 times the original function and moves down 3 down from the y-intercept.
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4.7: Transformations of Linear Functions

22. 4.7: Transformations of Linear Functions
Your Turn
Draw the function from the parent function y = x and the slope is 2/5 times the original function reflected and moves up 1 down from the y-intercept.
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4.7: Transformations of Linear Functions

23. 4.7: Transformations of Linear Functions
Function Notation
Known as “short-hand” writing
f(x) does NOT mean f times x, it is known as “f is a function of x”
When x is given, plug the equation in and solve
Simplify
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4.7: Transformations of Linear Functions

24. 4.7: Transformations of Linear Functions
Example 11
Given f(x) = x – 3, determine f(2).
(2)2
f(2) = 4 – 3
f(2) = 1
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4.7: Transformations of Linear Functions

25. 4.7: Transformations of Linear Functions
Example 12
Given f(x) = 2x – 10, determine f(6).
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4.7: Transformations of Linear Functions

26. 4.7: Transformations of Linear Functions
Your Turn
Given f(x) = –4x + 12, determine f(–8).
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4.7: Transformations of Linear Functions

27. 4.7: Transformations of Linear Functions
Example 13
Given f(x) = 2x – 5, find the value of x so that f(x) = 15. 15
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4.7: Transformations of Linear Functions

28. 4.7: Transformations of Linear Functions
Your Turn
Given f(x) = 4x + 3, find the value of x so that f(x) = –13.
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4.7: Transformations of Linear Functions

29. 4.7: Transformations of Linear Functions
Assignment
Worksheet
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4.7: Transformations of Linear Functions