Distance formula
Midpoint Formula
Center-Radius Form
R2= (x-h)2 + (y-k)2
If center is at origin then center-radius form becomes
X2 + y2 = r2
General Form of a Circle
Fix back to center radius from by completing the square
Function
Is a relation in which for each x-value there is exactly 1 y-value, so x-value cant repeat
Relation
Set of ordered pairs
Domain
Set of x-values
Range
Set of y-values
Vertical line test
The test if a graph is a function. If a vertical line inly passss through a line once then it is a function
Function Notation
when you use f(x) to indicate the outputs. Y = f(x)
Slope
y?-y?/x?-x?
point-slope form
slope-intercept form
y=mx+b
Standard form
Ax + Bx = C
Vertical Line
X = a
Horizontal Line
y=b
Parallel Lines
m1=m2
perpendicular lines
m1=-1/m2
Continuity
A function with no holes
|a|= b
If a=b or a=-b
|a|<b
If -b<a<b
|a|>b
If a<-b or a>b
|a|=|b|
If a=b or a=-b
Vertical stretch
If a>1 and y= a�f(x) then stretch vertically by factor of a
Vertical shrinking
If 0<a<1 and y=a�f(x) then compress vertically by factor of a
Horizontal Shrink
If a>1 and y=f(a�x) then compress horizontally by factor of 1/a
Horizontal Stretch
If 0<a<1 and y=f(a�x) then stretch horizontally by factor of 1/a.
Reflect on x-axis
If y= -f(x)
Reflect on y-axis
If
X-axis Symmetry
(a,b) is symmetric to (a,-b)
Y-axis symmetry
(a,b) is symmetric to (-a,b)
Origin symmetry
(a,b) is symmetric to (-a,-b)
Even function
F(x) = f(-x)
Odd Function
F(-x)= -f(x)
Vertical Shift
C>0, then move up c units; f(x)+c
C<0, then move down c units; f(x)-c
Horizontal Shifts
D>0, then shift to the left c units; f(x+d)
D<0, then shift to right c units; f(x-d)
Sum Function
(F+g)(x) = f(x)+g(x)
Difference Function
(F-g)(x) = f(x)-g(x)
Product Function
(FG)(x) = f(x)�g(x)
Quotient Function
(F/g)(x) = f(x)/g(x); g can't =0