38539666
Description
Mind Map by Nyla Brown, updated more than 1 year ago
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Created by Nyla Brown
almost 2 years ago
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Pre-Calc
- Quadratics
- Graphs
- Formulas
- f(x)=ax^2+bx+c
- f(x) = a(x-h)^2+k
- completing the square :
x = -b _/b^2 -4ac / 2a
- f(x)=ax^2+bx+c
- Graphs
- Linear Functions
- Formulas
- y=mx+b Examples:
y=5x-3, f(t) = 3t. h(x)=x.
y=3-x
- Increasing if m>0
decreasing if m<0.
constanct if m=0
- Parallel.
/ not
- f(x) = -2x+6.
g(x)=-2x-4
- f(x) = 3x+2.
g(x)=2x-2
- f(x) = -2x+6.
g(x)=-2x-4
- correlation coefficient
- r>0 --> increasing
- r<0 --> decreasing
- closer to 0 = more scattered
- closer to 1 or -1 = less scattered
- r>0 --> increasing
- y=mx+b Examples:
y=5x-3, f(t) = 3t. h(x)=x.
y=3-x
- Graphs
- Formulas
- Function Behavior
- Average rate of change
- (y2 - y1) / (x2 - x1)
- (y2 - y1) / (x2 - x1)
- Piecewise functions
(absolute functions)
- |x|= x. x≥0.
-x. x<0
- |x|= x. x≥0.
-x. x<0
- Inverse Functions
- f(x) = y, the inverse is f^-1(x)
- f^-1(x) = 1/f(x)
- f^-1(x) = 1/f(x)
- f(x) = y, the inverse is f^-1(x)
- Average rate of change
- Transformations
- Vertical and horizontal transformations
- shift
stretch
compress
flip
- shift
stretch
compress
flip
- Rational Functions
- Vertical
- x=0 as x approaches
0, f(x) tends to either
infinity or - infinity
- Removable Discontinuities
- x=0 as x approaches
0, f(x) tends to either
infinity or - infinity
- Horizontal
- y=b, the graph approaches the
line as the input
increases/decreases without
bound
- y=b, the graph approaches the
line as the input
increases/decreases without
bound
- Asymptotes
- f(x) = ((x+1)^2 (x-3)) / ((x+3)^2 (x-2))
- - at the x-int x=-1
corresponding to the
(x+1)^2 factor the
numerator, the graph
bounces - at the x-int x=3
corresponding to the
(x-3) factor the
numerator, the graph
passes through axis - at
x=-3 corresponds to the
(x+3)^2 factor of the the
the denominator, the
graph heads toward
positive infinity on both
sides - at x=2,
corresponds to the (x-2)
factor of the
denominator, the graph
heads to + infinity on the
left & - infinity on the
right
- - at the x-int x=-1
corresponding to the
(x+1)^2 factor the
numerator, the graph
bounces - at the x-int x=3
corresponding to the
(x-3) factor the
numerator, the graph
passes through axis - at
x=-3 corresponds to the
(x+3)^2 factor of the the
the denominator, the
graph heads toward
positive infinity on both
sides - at x=2,
corresponds to the (x-2)
factor of the
denominator, the graph
heads to + infinity on the
left & - infinity on the
right
- f(x) = ((x+1)^2 (x-3)) / ((x+3)^2 (x-2))
- Vertical
- Composite Functions
- Notation
- f of g = f(g(x))
- Domain
- f(x) = 5/x-1 , g(x) = 4/3x-2.
4/3x-2 = 1.
x=(- infinity, 2/3) U (2/3, 2) U (2,infinity)
- f(x) = 5/x-1 , g(x) = 4/3x-2.
4/3x-2 = 1.
x=(- infinity, 2/3) U (2/3, 2) U (2,infinity)
- f of g = f(g(x))
- Notation
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