Day 9 examples u2w14
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This document discusses translations of trigonometric functions including vertical shifts, horizontal shifts, vertical and horizontal stretches and compressions. It provides examples of trig functions with various translations including y=cos+2 for a vertical shift, 2y=sin(x+π) for a horizontal shift, f(x)=2cosx for a vertical stretch, and f(x)=sin(2x) for a horizontal compression with a new period.
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New day 9 examples
This document discusses translations of trigonometric functions including vertical shifts, horizontal shifts, and vertical/horizontal stretches or compressions. It provides examples of trig function transformations including changing the period or adding constants to vertically or horizontally shift the graph.
Day 9 examples
This document discusses translations, stretches, and compressions of trigonometric functions. It explains that y = sin(x) is equivalent to y = cos(π/2 - x) and y = cos(x) is equivalent to y = sin(π/2 - x). Vertical shifts are performed by adding or subtracting a constant, horizontal shifts use an added or subtracted constant inside the trig function's parentheses, and both horizontal and vertical shifts can be combined. Stretches and compressions are done by multiplying the trig function by a constant, which changes the period.
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1. Amplitude = 2, period = 1, horizontal translation = -4 (to the left), no vertical translation
2. Amplitude = 2, period = 120°, horizontal translation = 30° (to the right), vertical translation = -3 down
3. Amplitude = 3/2, period = 90°, no horizontal or vertical translation
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1) The document discusses the continuity of functions at a point and over an interval.
2) A function f is defined to be continuous at a point c if the limit of f(x) as x approaches c exists and is equal to f(c).
3) For a function to be continuous over an interval (a,b), it must be continuous at every point c within the interval.
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This document discusses translations of trigonometric functions including vertical shifts, horizontal shifts, and vertical/horizontal stretches or compressions. It provides examples of trig function transformations including changing the period or adding constants to vertically or horizontally shift the graph.
Day 9 examples
This document discusses translations, stretches, and compressions of trigonometric functions. It explains that y = sin(x) is equivalent to y = cos(π/2 - x) and y = cos(x) is equivalent to y = sin(π/2 - x). Vertical shifts are performed by adding or subtracting a constant, horizontal shifts use an added or subtracted constant inside the trig function's parentheses, and both horizontal and vertical shifts can be combined. Stretches and compressions are done by multiplying the trig function by a constant, which changes the period.
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1. Amplitude = 2, period = 1, horizontal translation = -4 (to the left), no vertical translation
2. Amplitude = 2, period = 120°, horizontal translation = 30° (to the right), vertical translation = -3 down
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Day 9 examples u2w14
- 1. Translations of Trig Functions We work with sin , cos only Vertical Shifts y = cos + 2
- 2. Horizontal Shifts 2 y = sin ( + )
- 3. Vertical/ Horizontal Stretch/ Compress ex. f(x) = 2cosx
- 4. Horizontal ex. f(x) = sin(2x) new period ex. Graph y = sin(x) New period
- 5. y = 2cos(x - ) - 1 2 y = 3sin2(x + ) - 1