Parent Graphs and Transformations

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Presentation transcript:

Parent Graphs and Transformations

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.

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) = x2 Jeff Bivin -- LZHS

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

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

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

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

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

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

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

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

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

Jeff Bivin -- LZHS

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

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

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

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

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

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

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

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

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

Jeff Bivin -- LZHS

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

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

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

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

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