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Warm up 8/2

Warm up 8/2. For each function, evaluate f(0), f(1/2), and f(-2) f(x) = x 2 – 4x f(x) = -2x + 1 If f(x) = -3x, find f(2x) and f(x-1) If f(x) = -2x + 3, find f(-2x) and f(2x-1). Answers. f(0)=0, f(1/2)=-1.75, f(-2)=12 =1, =0, =5 -6x , -3x + 3 4x + 3, -4x + 5.

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Warm up 8/2

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  1. Warm up 8/2 • For each function, evaluate f(0), f(1/2), and f(-2) • f(x) = x2 – 4x • f(x) = -2x + 1 • If f(x) = -3x, find f(2x) and f(x-1) • If f(x) = -2x + 3, find f(-2x) and f(2x-1)

  2. Answers • f(0)=0, f(1/2)=-1.75, f(-2)=12 • =1, =0, =5 • -6x , -3x + 3 • 4x + 3, -4x + 5

  3. Lesson 1.8 Transformations What is a translation? A translation is type of transformation where a graph is moved horizontally and/or vertically.

  4. Given the graph f(x)=(x-h)+k. • The graph moves horizontally (h) units and vertically (k) units • So f(x) = (x-h) + k Up/down Left/right Opposite of h

  5. Example 1: If the pre-image (original) is f(x) = 2x, • Describe the translation of the image of f(x) = 2(x – 3)+ 4. h = _____ which means _____________ k = _____ which means______________ 3 units to the right 3 4 units up 4 Example 2: Pre-image f(x) = 3x Image f(x) = 3(x+2) - 3 Describe the translation. left 2, down 3

  6. Example 3:Write the new equation.

  7. Example 4: Given f(x) = -4x. • A. Find f(x+5). -4(x+5) -4x – 20 • B. Find f(x-1)+6. -4 (x-1)+6 -4x +4 + 6 -4x + 10

  8. Example 5: • The pre-image is the blue function defined as y =x • What would be the equation of the red function? • What would be the equation of the green function? y = x + 3 y = (x – 3) – 1

  9. Another type of transformation is a REFLECTION…

  10. Translating and Reflecting Functions • Use a table to perform each transformation of • y = f(x). • Translation 2 units down • Reflection across the y-axis

  11. Stretches and Compressions

  12. Use a table to perform a horizontal compression of y = f(x) by a factor of ½.

  13. The Parent Function is the simplest function with the defining characteristics of the family. Functions in the same family are transformations of their parent functions. Lesson 1.9 - Intro to Parent Functions

  14. Parent Functions Family Rule Domain Range constant f(x) = c y = c Linear f(x) = x quadratic f(x) = x2 y ≥ 0

  15. Parent Functions Family Rule Domain Range Cubic f(x) = x3 Square Root x ≥ 0 y ≥ 0

  16. Identify the parent function and describe the transformation 1. 2. 3. f(x) = x2 Up 4 f(x) = x2 + 4 f(x) = x Down 3 f(x) = x-3

  17. Find the parent function and the transformation 1. Graph it Parent function: f(x) = x2 • Look at some points. Compare (2,2) with (2,4) from the parent function. • Both x values are the same. Starting with the 4 (parent function) what did we do to = 2? 4/2 = 2 So each y value was divided by 2. That is a vertical compression

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