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1.6 Graph Transformations

1.6 Graph Transformations. Shelby Sell Sammie Meddaugh Emily Wojahn. INTRODUCTION. http://www.youtube.com/watch?v=WXlll46ADAA. Vocabulary. Transformation: Functions that map real number to real numbers.

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1.6 Graph Transformations

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  1. 1.6 Graph Transformations Shelby Sell Sammie Meddaugh Emily Wojahn

  2. INTRODUCTION http://www.youtube.com/watch?v=WXlll46ADAA

  3. Vocabulary • Transformation: Functions that map real number to real numbers. • Rigid Transformations: Leave the side and shape of the graph unchanged (horizontal and vertical translations, reflections). • Non Rigid Transformations: Distort the shape of a graph (horizontal or vertical stretches and shapes).

  4. Translations • If c is a positive real number: Horizontal y= f(x-c) A translation to the right by c units y= f(x+c) A translation to the right by c units Vertical y= f(x) + c A translation up by c units y= f(x) - c A translation down by c units

  5. Examples y= abs(x) y= abs(x – 2) 2 y= x2 y= x2 + 3

  6. Reflections Across the x-axis (x,y) (x,-y) y= -f(x) Across the y-axis (x,y) (-x,y) y= f(-x) Through the origin (x,y) (-x.-y) y= -f(-x)

  7. Examples Reflection over y= x axis Reflection over y axis Reflection over x axis

  8. Stretches/Shrinks Horizontal Stretch/Shrink A stretch by a factor of c if c>1 A shrink by a factor of c if c<1 Vertical Stretch/Shrink A stretch by a factor of c if c> 1 A shrink by a factor of c if c<1 y= f (x/c) y= c f(x)

  9. Vertical Stretches Examples Graph y = 3x² y = x² Graph of y = x² Multiply all redvalues by 3 to get coordinates for the new graph. "Transformations on the Basic Parabola." W.A.E.C.E. Math Help. N.p., n.d. Web.

  10. Solution to y = 3x² Graph of y = x² with a stretch of 3.

  11. Combining Transformations in Order • 1.) Horizontal shift 2 units to the right y=(x-2) ² • 2.) Stretch Vertically by factor 3 y=3(x-2) ² • 3.) Vertical Translation 5 units up y=3(x-2) ² +5 Given y=x²

  12. 1.) Horizontal shift 2 units to the right y=(x-2) ²

  13. 2.) Stretch Vertically by factor 3 y=3(x-2) ²

  14. 3.) Vertical Translation 5 units up y=3(x-2) ² +5

  15. Absolute Value- Distance Y= f(x) Entire functions absolute value • (change negative y values to positive) Y= - f(x) Only Negative y values

  16. More absolute value

  17. 1.) Assessment 2 A) y = ½x2 + 2 B) y = 3x2 + 2 C) y = 3(x + 2)2 D) y = ½(x + 2)2

  18. 2.) 3 C) y = 2(x - 3)2 D) y = 2(x + 3)2 A) y = ½(x - 3)2 B) y = ½(x + 3)2

  19. 3.) C y = 2(x + 1)4 D y = 2(x - 1)4 A y = 0.5(x + 1)4 B y = 0.5(x - 1)4

  20. 4. Describe how the graph of y= x² can be transformed to the graph of the given equation Y=x²-3 A) Vertical translation up 3 units B) Horizontal translation to the right 3 units C) Horizontal translation to the left 3 units D) Vertical translation down 3 units

  21. 5.) • Given function f, which of the following represents a vertical stretch by a factor of 3. A) y=f(3x) B) y=3f(x) C) y=f(9x/3) D)y=f(x)/3

  22. 6.) • Given a function f, which of the following represents a vertical translation of 2 units upward, followed by a reflection across the y-axis. • A) y=f(-x) + 2 C) y= -f(x-2) • B) y= 2-f(x) D) f(x) -2

  23. 7.) • TRUE OR FALSE? • The function y=f(x+3) represents a translation to the right by 3 units of the graph of y = f(x).

  24. 8.) • TRUE OR FALSE? • The function of y=f(x)-4 represents a translation down 4 units of the graph of y=f(x)

  25. 9.) • Write an equation whose graph is • Y=x ²; a vertical stretch by a factor of 3, then shift right 4 units • A) y=3(x-4) ² C) y=3x ² -4 • B) y=-3x ² +4 D) y=3(x+4) ²

  26. 10.) • Write an equation whose graph is • Y= x ; a shift left 2 units, then a vertical stretch y a factor of 2, and finally a shift down 4 units. • A) 2 x+2 -4 C) 2 x-2 +4 • B) 2(x+2) -4 D) 3(x-2) +4

  27. Answers • 1.) B • 2.) A • 3.) A • 4.) D • 5.) B 6.) A 7.) False, it is translated left. 8.)True 9.) A 10.)A

  28. Sources http://www.mathopolis.com/questions/q.php?id=555&site=1&ref=/sets/function-transformations.html&qs=555_556_557_558_1191_2440_1192_2441_2442 http://departments.jordandistrict.org/curriculum/mathematics/secondary/impact/Algebra%20II/Ready%20for%20web%20site/zTransformationMatchingGame.pdf http://tutorial.math.lamar.edu/Classes/Alg/Transformations.aspx Pre calculus- Eighth edition book http://cheezburger.com/6321270784 "Transformations on the Basic Parabola." W.A.E.C.E. Math Help. N.p., n.d. Web.

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