10 shifting curves II

# 10 shifting curves II - y x 2 1 basic curve y x = 29 2 1 2...

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Shifting Curves II ( 29 y kf x = 1, curve is steeper k ( 29 1 y f x = intercepts asymptotes x 0 1, curve is shallower k < < (curve is stretched vertically) domain unchanged, range altered ( 29 y f kx = 1, curve is steeper k 0 1, curve is shallower k < < (curve is stretched horizontally) domain altered, range unchanged asymptotes intercepts x 1 1 y y < 1 1 y y < ( 29 OR y f x k =

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y x ( 29 e.g. on one graph draw i 1 ) , , 2 2 a y x y x y x = = = y x = 1 2 y x = 2 y x = 2 2 2 1 ) , , 2 2 b y x y x y x = = = y x 2 y x = 2 1 2 y x = 2 2 y x = 2 2 ( ) Sketch 1 4 y ii x + = y x 2 2 1. : 1 basic curve x y + = 1 1 –1 –1 2 2 2. , 2 4 2 y y k   = ∴ =  ÷   stretch vertically by a factor of 2
y x ( 29 e.g. on one graph draw i 1 ) , , 2 2 a y x y x y x = = = y x = 1 2 y x = 2 y x = 2 2 2 1 ) , , 2 2 b y x y x y x = = = y x 2 y x = 2 1 2 y x = 2 2 y x = 2 2 ( ) Sketch 1 4 y ii x + = y x 2 2 1. : 1 basic curve x y + = 1 2 –1 –2 2 2 2. , 2 4 2 y y k   = ∴ =  ÷   stretch vertically by a factor of 2

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y x 2 1. : basic curve y x = ( 29 2 1 2 iii y x = - 3. shift up 2 units 2. reflect in x axis 2
y x 2 1. : basic curve y x = ( 29 2 1 2 iii y x = - 3. shift up 2 units 2. reflect in x axis 2 4. x intercepts become asymptotes 2 - 2 5. y >1 become y <1 1 2 6. y <1 become y >1

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Unformatted text preview: y x 2 1. : basic curve y x = ( 29 2 1 2 iii y x =-3. shift up 2 units 2. reflect in x axis 2 4. x intercepts become asymptotes 2-2 5. y >1 become y <1 1 2 6. y <1 become y >1 ( 29 1 iv y x x = + y x 1. : 1 and draw the basic curves y x y x = = 2. add the y values together * choose key points first- x intercepts note: vertical asymptotes remain - points of intersection - as many other points as you need to work out the shape ( 29 1 iv y x x = + y x 1. : 1 and draw the basic curves y x y x = = 2. add the y values together * choose key points first- x intercepts note: vertical asymptotes remain - points of intersection - as many other points as you need to work out the shape Exercise 2J: 1, 2a, 3b, 4c, 5ac, 6b, 7ac, 8, 9...
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10 shifting curves II - y x 2 1 basic curve y x = 29 2 1 2...

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