1 / 8

1.7 Transformations of Functions

1.7 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) (this is the “slope”) 1) If | A | > 1 then it is vertically stretched.

rosa
Télécharger la présentation

1.7 Transformations of Functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. 1.7 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) (this is the “slope”) 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)) (sometimes we factor out the B term) 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.

  2. 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

  3. 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

  4. 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)  (5 , 6) f(x) – 3 (5 , 4)  (5 , 1) B) A • f(x) (multiply the y value by A) Example: 3 f(x) (5 , 4)  (5 , 12) ½ f(x) (5 , 4)  (5 , 2) –2 f(x) (5 , 4)  (5 , –8) C) f(x + C) (add –C to the x value) [change C’s sign] Example: f(x + 2) (5 , 4)  (3 , 4) (subtract 2) f(x – 3) (5 , 4)  (8 , 4) (add 3)

  5. 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)  (6 , 4) f(3x) (12 , 4)  (4 , 4) f (4(x)) (12 , 4)  (3 , 4) 2) If 0<B<1 (divide the x value by B) [flip & multiply] Example: f(½x) (12 , 4)  (24 , 4) f (¾(x)) (12 , 4)  (16 , 4) 3) If B is negative (follow the above rules for dividing) Example: f(-2x) (12 , 4)  (-6 , 4) f (-½(x)) (12 , 4)  (-24 , 4)

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

  7. 1.7 Transformations of Functions • Identify the parent function and describe the sequence of transformations. Horizontal shift eight units to the right Reflection in the x-axis, and a vertical shift of one unit downward

  8. H Dub • 1-7 Pg 80 #9-12 (parts A and B only), 13-18all, 19-39 EOO

More Related