Sequences, functions and graphs Flashcards
What is the term-to-term rule of 17,14,11,8…
Subtract 3
Un
a+(n-1)d
Sn
(n/2)(2a+(n-1)d)
Domain
Set of all inputs
Range
Set of all outputs
What is a function?
A mapping between elements of two sets
What is a one-to-one mapping?
Where every input has a unique output and every output has a unique input
What is a many-to-one mapping?
Where more than one input gives the same output
What is a one-to-many mapping?
Where one input gives more than one output
Find the inverse of (3x-1)/(2x+5)
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)
Gradient
dy/dx
Length of a line
root((x2-x1)2+(y2-y1)2)
Midpoint of a line
((x1+x2)/2,(y1+y2)/2)
y=f(x)+a
Up/down
y=f(ax)
Gradient
y=f(x+a)
Positive = left/negative = right
y=af(x)
Gradient and intercepts
Parallel line
m -> m
Perpendicular line
m -> -m-1
Differentiation
f(x)=axn
fI(x)=anxn-1
Chain rule
dy/dx f(g(x)) = fI(g(x))*gI(x)
Product rule
dy/dx u(x)v(x) = u(x)vI(x) + uI(x)*v(x)
Quotient rule
dy/dx u(x)/v(x) = (uI(x)*v(x) - u(x)vI(x))/v2(x)
If n is odd and f(n+1)(c) < 0
Local maximum
If n is even and f(n+1)(c) < 0
Decreasing inflection
If n is odd and f(n+1)(c) > 0
Local minimum
If n is even and f(n+1)(c) > 0
Increasing inflection
