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On graph paper, graph the following functions Transformations of Functions

I. There are 4 basic transformations for a function f(x). y = A f (Bx + C) + D A) f(x) + D (moves the graph + ↑ and – ↓) B) A f(x) 1) If | A | > 1 then it is vertically stretched. 2) If 0 < | A | < 1, then it’s a vertical shrink. 3) If A is negative, then it flips over the x-axis. C) f(x + C) (moves the graph +  and –  ) D) f(Bx) or f(B(x)) (factor out the B term if possible) 1) If | B | > 1 then it’s a horizontal shrink. 2) If 0 < | B | < 1, then it’s horizontally stretched. 3) If B is negative, then it flips over the y-axis. Attached to the y – vertical and intuitive Attached to the x – horizontal and counter-intuitive

1.7 Transformations of Functions II. What each transformation does to the graph. A) f(x) f(x) + D f(x) – D B) +A f(x) +A f(x) –A f(x). A > 1 0 < A < 1

1.7 Transformations of Functions II. What each transformation does to the graph. C) f(x) f(x + C) f(x – C) D) f(Bx) f(Bx) f(-Bx). B > 1 0 < B < 1

1.7 Transformations of Functions III. What happens to the ordered pair (x, y) for shifts. A) f(x) + D (add the D term to the y value) Example: f(x) + 2 (5, 4)  f(x) – 3 (5, 4)  B) A f(x) (multiply the y value by A) Example: 3 f(x) (5, 4)  ½ f(x) (5, 4)  –2 f(x) (5, 4)  C) f(x + C) (add –C to the x value) [change C’s sign] Example: f(x + 2) (5, 4)  (subtract 2) f(x – 3) (5, 4)  (add 3)

1.7 Transformations of Functions III. What happens to the ordered pair (x, y) for shifts. D) f(Bx) or f (B(x)) 1) If B > 1 (divide the x value by B) Example: f(2x) (12, 4)  f(3x) (12, 4)  f (4(x)) (12, 4)  2) If 0<B<1 (divide the x value by B) [flip & multiply] Example: f(½x) (12, 4)  f (¾(x)) (12, 4)  3) If B is negative (follow the above rules for dividing) Example: f(-2x) (12, 4)  f (-½(x)) (12, 4) 

1.7 Transformations of Functions f(x) is shown below. Find the coordinates for the following shifts. f(x) + 4 f(x) – 6 2 f(x) ½ f(x) -3 f(x) f(x + 4) f(x – 3) f(2x) f(½x) f(-3(x)) (-4,6) (-1,4) (1,7 ) (2,1) (-4,-4) (-1,-6) (1,-3) (2,-9) (-8,2) (-5,0) (-3,3) (-2,-3) (-1,2) (2,0) (4,3) (5,-3) (-4,4) (-1,0) (1,6) (2,-6) (-4,1) (-1,0) (1, 3 / 2 ) (2,- 3 / 2 ) (-4,-6) (-1,0) (1,-9) (2,9) (-2,2) (- 1 / 2,0) ( 1 / 2,3) (1,-3) (-8,2) (-2,0) (2,3) (4,-3) ( 4 / 3,2) ( 1 / 3,0) (- 1 / 3,3) (- 2 / 3,-3)

Identify the parent function and describe the sequence of transformations. 1.7 Transformations of Functions Horizontal shift eight units to the right Reflection in the x-axis, and a vertical shift of one unit downward or y-axis!

Identify the parent function and describe the sequence of transformations. Parent Function Left 2 Horizontally compressed by a factor of 1/2 1.7 Transformations of Functions Always factor If possible!

Identify the parent function and describe the sequence of transformations. Flip over y-axis and right 4 If x is negated, factor out a negative! 1.7 Transformations of Functions

When graphing, perform non-rigid transformations 1 st and rigid transformations last That means stretch / compress / reflect before moving left / right / up / down Then find a few points and perform transformations on those points. Ex: Graph

Practice Ex: Graph

H Dub 1-7 Page 80 #9-12 (parts A and B only), all, 19-39EOO