This is a draft cheat sheet. It is a work in progress and is not finished yet.
Lines
Slope = m |
Slope-intercept: y=mx+b |
m = dy/dx |
Point-slope: y-y1=m(x-x1) |
Parallel: m=m |
General Form: Ax+By+C=0 |
Perpendicular: m=-(1/m) |
Distance= sqr((x2-x1)2+(y2-y1)2) |
Absolute Values and Inequalities
Absolute Value is distance from 0 |
( = not included |
labl=lal*lbl |
[ = included |
la-bl=lb-al |
Infinities use ( in notation |
Check inequality problems for both positive and negative answers, and that the answers make sense in original problem |
Use number lines for systems of equations |
Exponents
ax *ay = ax+y |
ax / ay = ax-y |
(ax)y=axy |
(ab)x=ax * bx |
(a/b)x = (ax/bx) |
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Functions
In functions, each x value has only one y value |
Use vertical line test to determine if a graph shows a function |
(f+g)(x)=f(x)+g(x) |
(f-g)(x)=f(x)-g(x) |
(fg)(x)=f(x)*g(x) |
(f/g)(x)=f(x)/g(x), g(x)=0 |
(fg) =f(g(x)) |
For inverse functions, f(g(x))=x |
Logarithms
Assume all these logs have a base of a |
y=log(x) when ay=x |
log(xy) = log(x)+log(y) |
log(x/y)=log(x)-log(y) |
log(x)n=n*log(x) |
log(1)= 0, log(a)=1 |
Natural Log and e
ln and e are inverse operations and cancel each other out |
ln(xy)=ln(x)+ln(y) |
ex * ey =ex+y |
ln(x/y)=ln(x)-ln(y) |
ex \ ey =ex-y |
ln(x)n=n*ln(x) |
(ex)y= exy |
Change of Base: log(base a)(x) = ln(x)/ln(a) |
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Trigonometric Functions and Graphs
Function |
Graph Descriptions
(Without Transformations) |
sinx= O/H |
Sinusoidal, Starts at 0 |
cosx= A/H |
Sinusoidal, Starts at A |
tanx= O/A |
Positive cubic functions |
cscx= H/O |
Positive and Negative Parabolas
(Starts at 0) |
secx= H/A |
Positive and Negative Parabolas
(Doesn't start at 0) |
cotx= A/O |
Negative cubic functions |
Trig functions take an angle and find the corresponding ration of the sides |
Inverse functions take the ration of the sides and find the corresponding angle |
Graphs
Increasing: m>0 |
Decreasing: m<0 |
Constant: m=0 |
Minimum: Decreasing to Increasing |
Maximum: Increasing to Decreasing |
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