Sequences, functions and graphs Flashcards

1
Q

What is the term-to-term rule of 17,14,11,8…

A

Subtract 3

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2
Q

Un

A

a+(n-1)d

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3
Q

Sn

A

(n/2)(2a+(n-1)d)

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4
Q

Domain

A

Set of all inputs

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5
Q

Range

A

Set of all outputs

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6
Q

What is a function?

A

A mapping between elements of two sets

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7
Q

What is a one-to-one mapping?

A

Where every input has a unique output and every output has a unique input

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8
Q

What is a many-to-one mapping?

A

Where more than one input gives the same output

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9
Q

What is a one-to-many mapping?

A

Where one input gives more than one output

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10
Q

Find the inverse of (3x-1)/(2x+5)

A

x=(3y-1)/(2y+5)
2yx+5x=3y-1
2yx-3y=-1-5x
y(2x-3)=-1-5x
y=(-1-5x)/(2x-3)
fI(x)=(1+5x)/(3-2x)

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11
Q

Gradient

A

dy/dx

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12
Q

Length of a line

A

root((x2-x1)2+(y2-y1)2)

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13
Q

Midpoint of a line

A

((x1+x2)/2,(y1+y2)/2)

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14
Q

y=f(x)+a

A

Up/down

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15
Q

y=f(ax)

A

Gradient

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16
Q

y=f(x+a)

A

Positive = left/negative = right

17
Q

y=af(x)

A

Gradient and intercepts

18
Q

Parallel line

A

m -> m

19
Q

Perpendicular line

A

m -> -m-1

20
Q

Differentiation

A

f(x)=axn
fI(x)=anxn-1

21
Q

Chain rule

A

dy/dx f(g(x)) = fI(g(x))*gI(x)

22
Q

Product rule

A

dy/dx u(x)v(x) = u(x)vI(x) + uI(x)*v(x)

23
Q

Quotient rule

A

dy/dx u(x)/v(x) = (uI(x)*v(x) - u(x)vI(x))/v2(x)

24
Q

If n is odd and f(n+1)(c) < 0

A

Local maximum

25
Q

If n is even and f(n+1)(c) < 0

A

Decreasing inflection

26
Q

If n is odd and f(n+1)(c) > 0

A

Local minimum

27
Q

If n is even and f(n+1)(c) > 0

A

Increasing inflection