f(x)= 2x 2 +x f(x)= x 3 f(x)= x 3 +2

Transcription

1 Show that the following functions 1. Warm up Functions even and odd 2. Review Problems From Friday 3. Inverse Functions are even, odd or neither using function notation. f(x)= 2x 2 f(x)= 2x 2 +x f(x)= x 3 f(x)= x

2 f(-x)= f(x) even f(-x)= -f(x) odd f(-x)= 2(-x) 2 = 2x 2 Even f(x)= 2x 2 f(-x)= 2(-x) 2 +(-x) = 2x 2 -x neither f(x)= 2x 2 +x f(-x)= (-x) 3 = -x 3 Odd f(x)= x 3 f(-x)= (-x) 3 +2=-x 3 +2 Neither f(x)= x

3 f(-x)= f(x) even f(-x)= 2(-x) 2 = 2x 2 f(-x)= -f(x) odd f(x)= 2x 2 f(-x)= 2(-x) 2 +(-x) = 2x 2 -x f(x)= 2x 2 +x f(x)= x 3 f(x)= x 3 +2 f(-x)= (-x) 3 = -x 3 f(-x)= (-x) 3 +2=-x

4 Oct 9 11:20 AM 4

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6 cosine is negative in the second quadrant 6

7 sine is negative in the third quadrant 7

8 Pythagorean Identities 8

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11 It is possible to consider the sine or cosine functions for this situation. Max Temp about 86 Min Temp about 50 Period = 12 months You must consider the phase shift, amplitude, flip and or vertical shift 11

12 Find the midline add the max and min then divide Use the midline to find the the amplitude Max Temp about 86 Min Temp about 50 Period = 12 months Midline is 68 D = 68 Use the 12 month period to find the shift 12

13 Max Temp about 86 Min Temp about 50 Period = 12 months Find the midline add the max and min then divide Midline is 68 D = 68 Subtract to find the amplitude. Use the midline to find the the amplitude Use the 12 month period to find the shift A can be poistive or negative 18 If you use positive 18 you need a phase shift to write your equation. 18 will be a flip of the parent function 13

14 Max Temp about 86 Min Temp about 50 Period = 12 months Find the midline add the max and min then divide Midline is 68 A= 18 D = 68 or A = 18 Subtract to find the amplitude. Use the midline to find the the amplitude Use the 12 month period to find the shift A can be poistive or negative 18 If you use positive 18 you need a phase shift to write your equation. 18 will be a flip of the parent function 14

15 Max Temp about 86 A= 18 Midline is 68 Min Temp about 50 or D = 68 A = 18 Period = 12 months To find B the period Find the midline add the max and min then is 12 months. divide Use the midline to find the the amplitude Use the 12 month period to find the shift C will be either 0 or 6 months 15

16 Max Temp about 85 Min Temp about 31 Period = 12 months Find the midline add the max and min then divide Midline is 68 A= 18 D = 68 or A = 18 To find B the period is 12 months. Use the midline to find the the amplitude Use the 12 month period to find the shift We will use B positive C will be either 0 or 6 months for Cosine 16

17 Max Temp about 85 Min Temp about 31 Period = 12 months Find the midline add the max and min then divide Midline is 68 D = 68 if the shift is 6 then calculate C. A= 18 or A = 18 Or C = 0 Use the midline to find the the amplitude Use the 12 month period to find the shift 17

18 Max Temp about 85 Min Temp about 31 Period = 12 months Midline is 68 D = 68 A= 18 or A = 18 Or C = 0 18

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20 The wheel rotates at a rate of 2 revolutions every 6 minutes. (Don t worry about the distance the seat is hanging from the bar.) Let the center of the wheel represent the origin of the axes. Two revolutions in 6 minutes which means on revolutions is one period and therefore a period is 3 minutes. D = 70 A = 60 Since the radius is 60 the maximum height is because the wheel is 10 feet off the ground. The Amplitude will be 60 The Midline will be 70 20

21 1. Write a function that describes Sydney s height above the ground as a function of the number of seconds since she was ¼ of the way around the circle (at the 3 o clock position). In the given situation the sine starts at zero. So I will use the sine 21

22 2. How high is Sydney after 1.25 minutes? x=

23 Sydney s friend got on after Sydney had been on the Ferris wheel long enough to move a quarter of the way around the circle. How would a graph of her friend s ride compare to the graph of Sydney s ride? What would the equation for Sydney s friend be? The new function would have a shift that is 1/4 around the circle. 23

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25 Due Tues :Complete Unit Circle Due Wed: Text Book P : 21-25,29-35,37 P.277: 27,29,31,33,35 Due Friday: Graphing Task 25

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27 Mar 13 11:25 AM 27

28 Mar 13 11:25 AM 28

29 Mar 13 4:57 PM 29

30 Mar 13 4:57 PM 30

31 Mar 14 9:03 AM 31