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# Mathematics portfolio - Translations.

Extracts from this document...

Introduction

Man Ju    Y12D

## Translations

1. 2. is the effect of translation vector            of . It moves up 2 units. is the effect of translation vector            of . It moves up 4 units. is the effect of translation vector            of . It moves down 3 units.

3.  + 3 is the effect of translation vector             of . It moves up 3 units. -1 is the effect of translation vector             of . It moves down 1 unit.

4.        Curves move either up or down vertically. The units they move is according to the number                   after x2 in the equation . If the number is positive, the curve will be pulled upwards. If the number is negative, the curve will be pulled downwards.

5. f(x) = sinx –2 is the effect of translation vector            of f(x) = sinx. It moves down 2 units.

This has the same effect with the previous examples. The unit it moves is according to the

number after sinx in the equation f(x) = sinx     c. If the number is positive, the curve will be pulled upwards.

Middle

. If the number is positive, the curve will shift to the left. If the number is negative, the curve will shift to the right.  = sin (x-90)2  is the effect of translation vector             of = sinx. It moves right 90 units. This has the same effect with the previous examples. The units the curve moves are according to the number after x in the equation = sin(x     c). If the number is positive, the curve will shift to the left. If the number is negative, the curve will shift to the right. Therefore the generalization extend to any function .

10.        i. Shift 3 to the right and 5 downwards.

ii. Shift 2 to the left and 1 downwards.

iii. , (first complete the square).

y = ( x – 2 )2 – 4 + 3

y = ( x – 2 )2 – 1

Shift 2 to the right and 1 downwards.

Stretches

1. 2. is the effect of one way stretch along the y axis, scale factor 2 of . is the effect of one way stretch along the y axis, scale factor 4 of . Conclusion  = sin(2x)is the effect of one way stretch along the x axis sxale factor ½. This has the same effect with the previous examples. Scale factor is determined by the number in front of x in the equation = sin(    a sinx). If the number is bigger than 1 after it has been squared, the curve will be stretched inwards. If the number is smaller than 1 after it has been squared, the curve will be stretched outwards. Therefore the generalization extend to any function .

All Together!

10.        i. y = 2 (x2 + 2x –1/2)

y = 2 [ (x+1)2 - 1 - 1/2 ]

y = 2 [ (x+1)2 – 3/2 ]

Therefore a = 2

p = 1

q = -3/2

ii. 1. y = x2 shift 1 to the left to become y = (x+1)2

2. y = (x+1)2 shift 3/2 down to become y = (x+1)2 –3/2

3. y = (x+1)2 –3/2 stretched one way, scale factor 2 along the y axis to become

y = 2[(x+1)2 –3/2]

iii. y = 3 (x2 - 2x – 2/3)

y = 3 [ (x -1)2 - 1 – 2/3 ]

y = 3 [ (x -1)2 – 5/3 ]

Therefore a = 3

p = -1

q = -5/3 1. y = x2 shift 1 to the right to become y = (x-1)2
2. 2. y = (x-1)2 shift 5/3 down to become y = (x-1)2 –5/3
3. y = (x-1)2 –5/3 stretched one way, scale factor 3 along the y axis to become

y = 3[(x-1)2 –5/3]

This student written piece of work is one of many that can be found in our AS and A Level Core & Pure Mathematics section.

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