1. Worksheet Key 1) (–∞, –4] 2) [–1, ∞) 3) (–4, ∞) 4) (–∞, –2) 5)
(–∞, –5) 6)
(–8, ∞) 7)
(–36, ∞) 8)
(–16, ∞) 9)
(–∞, 6/5)
10)
(4, ∞)
11)
(–∞, 23/3)
12)
(–74/7, ∞)
13)
x > 75
14)
x < 77
8/13/ :15 AM
Parent Functions

2. Quiz
When done, turn in the quiz to the back and pick up a parent function chart and fill it out
8/13/ :15 AM
Parent Functions

3. 8/13/ :15 AM
Parent Functions

4. Revised ©2014 Viet.dang@humble.k12.tx.us
Parent Functions
Revised ©2014
8/13/ :15 AM
Parent Functions

5. What is a Parent Function?
A. The parent function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent function. B. There are main parent functions that are utilized through Algebra. They are the following:
8/13/ :15 AM
Parent Functions

6. Parent Functions Family Rule Constant f(x) = c Linear f(x) = x
Quadratic
f(x) = x2
Cubic
f(x) = x3
Graph
Table x –2 –1 1 2 y c x –2 –1 1 2 y x –2 –1 1 2 y 4 x –2 –1 1 2 y –8 8
Domain
Range
8/13/ :15 AM
Parent Functions

7. Parent Functions Family Rule Square Root f(x) = √x Cubic Root
Reciprocal/Rational
f(x) = 1/x
Absolute Value
f(x) = |x|
Exponential
f(x) = 2x
Graph
Table x 1 4 9 y 2 3 x –8 –1 1 8 y –2 2 x –2 –1 1 2 y
–.5
DNE .5 x –2 –1 1 2 y x –2 –1 1 2 y
1/4
1/2 4
Domain
Range
8/13/ :15 AM
Parent Functions

8. Scale Factor (Scalar)
The equation will now look like, y = a(x – h) + k
_h_ stands for the Horizontal Shift
_k_ stands for the Vertical Shift
The standard points will now be adjusted by the scalar (a)
Multiply a with the x–values of the standard points.
The scalar does not affect the new origin.
8/13/ :15 AM
Parent Functions

9. Vertical Shifts of A
For shifts of A of ax2 + bx + c = y, the bigger the A, the smaller the graph gets.
8/13/ :15 AM
Parent Functions

10. Vertical Shifts of C
For shifts of C of ax2 + bx + c = y, the change of the C, the y–intercept shifts up or down
8/13/ :15 AM
Parent Functions

11. Horizontal Shifts ADDED, it moves to the LEFT
For shifts of A of f(x)= a(x – h)2 + k, the change of the h, the graph shifts either left or right
If the equation is…
ADDED, it moves to the LEFT
SUBTRACTED, it moves to the RIGHT
8/13/ :15 AM
Parent Functions

12. Reflection Shifts
For horizontal shifts of f(x)= –a(x – h)2 + k or others, the change of the a, the graph shifts reflects on the axis
8/13/ :15 AM
Parent Functions

13. Let’s Dance
8/13/ :15 AM
Parent Functions

14. Aerobic Moves
8/13/ :15 AM
Parent Functions

15. Example 1
Given the graph of f(x) = x – 3, determine the domain, range, and transformation change in Interval Notation
8/13/ :15 AM
Parent Functions

16. Example 2
Given the graph of f(x) = 2x, determine the domain, range, and transformation change in Interval Notation
8/13/ :15 AM
Parent Functions

17. Your Turn
Given the graph of f(x) = (1/2)x + 5, determine the domain, range, and transformation change in Interval Notation
8/13/ :15 AM
Parent Functions

18. Example 3
Given the graph of f(x) = (x + 1)2 – 3, determine the domain, range, and transformation change in Interval Notation
8/13/ :15 AM
Parent Functions

19. Example 4
Given the graph of f(x) = –|x – 2| + 4, determine the domain, range, and transformation change in Interval Notation
8/13/ :15 AM
Parent Functions

20. Example 5
Given the graph of f(x) = y = –2(x – 3)3 + 1, determine the domain, range, and transformation change in Interval Notation
8/13/ :15 AM
Parent Functions

21. Your Turn
Given the graph of f(x) = (x – 1)2 – 4, determine the domain, range, and transformation change in Interval Notation
8/13/ :15 AM
Parent Functions

22. Example 6
Given a linear parent function, the shift of the equation is 4 units up, determine the equation.
8/13/ :15 AM
Parent Functions

23. Example 7
Given an absolute value parent function, the shift of the equation is 4 units down and 2 units to the left, determine the equation.
8/13/ :15 AM
Parent Functions

24. Your Turn
Given a quadratic parent function, the shift of the equation is 3 units down and 4 units to the left, determine the equation.
8/13/ :15 AM
Parent Functions

25. Assignment
Worksheet
8/13/ :15 AM
Parent Functions