1. Absolute Value Function
Do Now
Roughly sketch the following different types of graphs. Don’t make them perfect! Do your best.
Linear function
Quadratic Function
Cubic Function
Square Root Function
Cube Root Function
Absolute Value Function

2. Appendix D Graphing Techniques Day 1
Objective: SWBAT review graphing techniques of stretching & shrinking, reflecting, symmetry and translations.

3. Parent Functions
The most basic function within a function family that all other functions are based off of.
The following slides represent the parent functions with their corresponding function families.

4. Identity Function
Domain: all reals
Range: all reals

5. Square Function (a quadratic formula)
Domain: all reals
Range: [0, ∞)

6. Cube Function
Domain: all reals
Range: all reals

7. Square Root Function
Domain: [0, ∞)
Range: [0, ∞)

8. Cube Root Function
Domain: all reals
Range: all reals

9. Absolute Value Function
Domain: all reals
Range: [0, ∞)

10. Vertical Shift
The graph of y = f(x) + k can be obtained from the graph of y = f(x) by vertically translating (shifting) the graph of the latter upward k units if k is positive and downward |k| units if k is negative.

11. Graph y = |x| and y = |x| + 4. Describe the transformation from the parent function.
Create a table of 5 points.
Choose the middle point so that it makes the inside of the absolute value zero!
This point is called your vertex. (This applies for absolute value and quadratic functions.)

12. Vertical Shift

13. Graph the following two functions: 𝒚= 𝒙 𝟐 and 𝒚= 𝒙 𝟐 −𝟓
Graph the following two functions: 𝒚= 𝒙 𝟐 and 𝒚= 𝒙 𝟐 −𝟓. Describe the transformation from the parent function.

14. Horizontal Shift
The graph of y = f(x + h) can be obtained from the graph of y = f(x) by horizontally translating (shifting) the graph of the latter h units to the left if h is positive and |h| units to the right if h is negative.

15. Graph y= |x + 4|. Describe the transformation from y = |x|.

16. Graph y = |x - 5|. Describe the transformation from y = |x|.

17. Graph y = |x - 2|+3. Describe the transformation from y = |x|.

18. Describe the transformations for the following functions from their parent functions.
𝑓 𝑥 = 𝑥 2 +16
𝑔 𝑥 = 𝑥−9 2 −8
ℎ 𝑥 = 𝑥+2 −3
𝑓 𝑥 = 𝑥−3 +8

19. Write a NEW function g(x) based on the following transformations to the given function.
𝑓 𝑥 = 𝑥 translated 2 units right and 3 units down
𝑓 𝑥 = 𝑥 translated 2 units down and 1 units right
𝑓 𝑥 = 𝑥−3 2 −7--- translated 5 units up and 7 units left

20. Horizontal & Vertical Shifts
If the shift happens outside the function, it is vertical. If the shift happens inside the function, it is horizontal.

21. Homework:
Translations on Parent Functions Review Worksheet
# 4, 6, 10, 13, 15, 16