1. Parent Graphs and Transformations

2. Standards
MM1A1. Students will explore and interpret the characteristics of functions, using graphs, tables, and simple algebraic techniques.
b. Graph the basic functions where n = 1 to 3, , , and .
c. Graph transformations of basic functions including vertical shifts, stretches, and shrinks, as well as reflections across the x- and y-axis. [Previewed in this unit.]
d. Investigate and explain the characteristics of a function: domain, range, zeros, intercepts, intervals of increase and decrease, maximum and minimum values, and end behavior.
e. Relate to given context the characteristics of a function, and use graphs and tables to investigate its behavior.

3. General Form f(x)= a (x – h) + k Linear f(x)= a (x – h) + k
Quadratic f(x)= a (x – h)2 + k
Cubic f(x)= a (x – h)3 + k
Absolute Value f(x)= a | (x – h) | + k
Square root/ Radical
Rational

4. What does each letter do?
a – if |a| > 1 there is a vertical stretch
– if 0 < |a| < 1 there is a vertical shrink
- If a = negative there is a reflection
h – shifts the graph right and left (horizontally shifts)
k – shifts graph up and down (vertical shift)

5. 1. f(x) = x2
Jeff Bivin -- LZHS

6. 2. f(x) = (x + 4)2 - 2 (0,14) x + 4 = 0 x = -4 4 2 (-4,-1)
Jeff Bivin -- LZHS

7. 3. f(x) = x2 + 3
x = 0
(0,3) 3
Jeff Bivin -- LZHS

8. 4. f(x) = (x + 5)2 - 4 (0,21) x + 5 = 0 x = -5 5 4 (-5,-4)
Jeff Bivin -- LZHS

9. 5. f(x) = -2(x + 3)2 + 5 (-3,5) x + 3 = 0 x = -3 5 3 stretch (0,-13)
Jeff Bivin -- LZHS

10. 6. f(x) = x3
Jeff Bivin -- LZHS

11. 7. f(x) = -(x + 2)3
x + 2 = 0
flip
x = -2 2
Jeff Bivin -- LZHS

12. 8. f(x) = 2x3 + 3
(0,3)
x = 0 3
stretch
stretch
Jeff Bivin -- LZHS

13. 9. f(x) = (x + 3)3 - 2 (0,25) x + 3 = 0 x = -3 3 2 (-3,-2)
Jeff Bivin -- LZHS

14. 10. f(x) = -3(x + 2)3 + 1 x + 2 = 0 x = -2 (-2, 1) 2 1 flip stretch
(0,-23)
Jeff Bivin -- LZHS

15. Jeff Bivin -- LZHS

16. x - 3 = 0
x = 3 3 4
stretch
stretch
Jeff Bivin -- LZHS

17. flip
x = 0
(0, 2) 2
Jeff Bivin -- LZHS

18. x + 3 = 0
flip
x = -3 4 3
(-3, -4)
stretch
stretch
Jeff Bivin -- LZHS

19. x - 3 = 0
flip
x = 3
(3, 2) 3 2
Jeff Bivin -- LZHS

20. 16. y =|x|
Jeff Bivin -- LZHS

21. 17. y = -|x-3|+2 x-3 = 0 x = 3 (3, 2) 2 3 flip (0, -1)
Jeff Bivin -- LZHS

22. 18. y = 3|x+1|-2 x+1 = 0 x = -1 (0, 1) 2 1 stretch stretch (-1, -2)
Jeff Bivin -- LZHS

23. 19. y = -3|x-2| + 4 (2, 4) x-2 = 0 x = 2 4 2 stretch (0, -2) stretch
Jeff Bivin -- LZHS

24. y = |-3x|
(0, 0)
squeeze
squeeze
Jeff Bivin -- LZHS

25. Jeff Bivin -- LZHS

26. x + 1 = 0
(0, 3)
x = -1
y = 2 1 2
x = -1
Jeff Bivin -- LZHS

27. x - 2 = 0
x = 2
y = 3
(0, 5/2) 2 3
x = 2
Jeff Bivin -- LZHS

28. x - 3 = 0
x = 3 3 1
y = -1
(0, -4/3)
x = 3
Jeff Bivin -- LZHS

29. flip
x + 2 = 0
y = 3
x = -2
(0, 5/2) 2 3
x = -2
Jeff Bivin -- LZHS

30. flip
x - 1 = 0
(0, 3)
x = 1
y = 2 1 2
x = 1
Jeff Bivin -- LZHS