Parent Graphs and Transformations Standards MM 1 A

Parent Graphs and Transformations

Standards • MM 1 A 1. 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 xand 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.

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

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)

1. f(x) = x 2 Jeff Bivin -- LZHS

2. f(x) = (x + Jeff Bivin -- LZHS 2 4) -2

3. f(x) = Jeff Bivin -- LZHS 2 x +3

4. f(x) = (x + Jeff Bivin -- LZHS 2 5) -4

5. f(x) = -2(x + Jeff Bivin -- LZHS 2 3) +5

6. f(x) = x 3 Jeff Bivin -- LZHS

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

8. f(x) = Jeff Bivin -- LZHS 3 2 x +3

9. f(x) = (x + Jeff Bivin -- LZHS 3 3) -2

10. f(x) = -3(x + Jeff Bivin -- LZHS 3 2) +1

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

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

17. Jeff Bivin -- LZHS y = -|x-3|+2

18. Jeff Bivin -- LZHS y = 3|x+1|-2

19. Jeff Bivin -- LZHS y = -3|x-2| + 4

20. Jeff Bivin -- LZHS y = |-3 x|

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS

Jeff Bivin -- LZHS