Linear
F(x)= x
Domain: (-?���,?���)
Range: (-?���,?���)
Quadratic
F(x)= x^2
Domain: (-?���,?���)
Range: [0,?���)
Cubic
F(x)= x^3
Domain: (-?���,?���)
Range: (-?���,?���)
Rational inverse
F(x)= 1/x
Domain: (-?���,0)U(0,?���)
Range: (-?���,0)U(0,?���)
Rational squared
F(x)= 1/x^2
Domain: (-?���,0)U(0,?���)
Range: (0,?���)
Absolute value
F(x)= |x|
Domain : (-?���,?���)
Range : [0,?���)
Square root
F(x)=?��??�X
Domain: [0,?���)
Range: [0,?���)
Exponential
F(x)= e^x
Domain: (-?���,?���)
Range: (0,?���)
Natural log
F(x)= In x
Domain: (0,?���)
Range: (-?���,?���)
Sine
F(x)= sin x
Domain: (-?���,?���)
Range: [-1,1]
quadratic formula
compound interest formula
simple interest formula
complex numbers
discriminant formula
if D> 0: 2 real solutions
if D<0: 2 non-real solutions
if D=0 : exactly 1 solution
factor by grouping
inequality signs
greater/ less than or equal to
filled in circle
greater than/ less than
open circle
quadrants
midpoint formula
distance formula
standard form of a circle
center of the circle: (h,k)
radius: r
general form of a circle
positive slope
negative slope
zero slope
slope
m= rise/ run
point slope form
m: slope of the line
slope intercept form
m: slope
b: y intercept
standard form slope and y intercept
Ax + By = C slope: m= -A/B
y intercept: C/B
horizontal line equation
y = b b: the y coordinate of any point on the line
two non-vertical lines are parallel if
they have the same slopes
two non-vertical lines are perpendicular if
the product of their slopes is -1
vertical line test
even function
symmetric across the y axis
odd function
symmetric across the origin
constant function
identity function
square function: f(x)= x^2
cube function: f(x)= x^3
absolute value function: f(x)= lxl
square root function: f(x)= sqrtx
cube root function: f(x)= 3sqrtx
reciprocal function: f(x)= 1/x
greatest integer function
y= -f(x)
reflection about the x-axis
y= f(-x)
reflection about the y-axis
vertical stretch y= af(x)
multiply each y coordinate by a
horizontal compression
a>1: divide each x coordinate of y= f(x) by a
horizontal stretch
0<a<1: divide each x coordinate of y= f(x) by a
finding the inverse of a function
quadratic function
the porabola opens up if
the leading coefficient a>0
the porabola opens down if
the leading coefficient a<0
the standard form of a quadratic function
the vertex of a porabola: (h,k)
vertex formula
long division
synthetic division
can only be used if divided by form (x-c)
complex conjugate pairs theorem
inverse variation
continuous compound interest formula
A: total amount after t years
P: original investment
r: interest rate per year
n: number of times interest is compounded per a year
t: number of years
method of relating the bases
if b^u= b^v then u=v