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13.6 Homework

13.6 Homework. 9) P = π 10) P = π /2 11) P = π /5; ± π /10 12) P = (2 π )/3; ± π /3 13) P = π /4; ± π /8 14) P = (3 π 2 )/2; ±(3 π 2 )/4 15) 16) 17) 18). Section 13.7. Translating Sine and Cosine Functions. Translating Functions. y = a • f ( b ( x – h )) + k

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13.6 Homework

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  1. 13.6 Homework 9) P = π 10) P = π/2 11) P = π/5; ± π/10 12) P = (2 π)/3; ± π/3 13) P = π/4; ± π/8 14) P = (3π2)/2; ±(3π2)/4 15) 16) 17) 18)

  2. Section 13.7 Translating Sine and Cosine Functions

  3. Translating Functions y = a •f (b (x – h)) + k • a – vertical stretch • b – horizontal stretch • h – horizontal shift • k – vertical shift • The same translating rules apply to all functions • Each constant in the equation does the same job

  4. Phase Shift What is the value of h in each function? Describe the phase shift in terms of left or right. • g (x) = f (x + 1) h = –1; left 1 • m (x) = f (x – 3) h = 3; right 3 • y = sin (x + π) h = –π; left π • In periodic functions the horizontal shift is also called the “phase shift” • The phase shift tells us how far around the unit circle we need to start to have the same results

  5. Graphing Translations A phase shift moves the graph sideways k moves the graph up or down

  6. Translate a Function Translate the graph f (x) to be f (x – 1) 2 4

  7. Parent Functions • Parent Functions: • y = a sin bx • y = a cos bx • Translated Functions • y = a sin b (x – h) + k • y = a cos b (x – h) + k • Translating Rules • |a| = amplitude • = period (x is in radians and b > 0) • h = phase shift, or horizontal shift • k = vertical shift 2π b

  8. Homework (part 1) For the next class complete #3 – 30 every 3rd, starting on page 746.

  9. Homework (part 1) Answers 3) h = 1.6; right 1.6 6) h = 5π/7; right 5π/7 9) 12) 15) 18) Amp: 4, Per: π, Left 1, down 2 21) 24) 27) 30)

  10. Writing Equations • We can use the values for period, amplitude, phase shift, and vertical shift • Begin with the parent function and place the values for a, b, h, and k in their appropriate places Write an equation for each translation: • y = sin (x), 4 units down y = sin (x) – 4 • y = cos (x), π units left y = cos (x + π) • y = sin (x), period of 3, amp of 2, right π/2, down 1 y = 2 sin (x – π/2) – 1 2π 3

  11. Weather Cycles Plot a graph of the data (in degrees) and write a cosine function to model the information. Let a > 0. y = 21 cos (x – 180) + 63 50˚F A M J A S O N D J F M J J

  12. Homework (part 2) For the next class complete #34 – 43 starting on page 746.

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