Algebra 2 unit 8

STUDY
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Terms in this set (...)

Radical Exponents
^n√a=^1/n
Negative even powdered roots
No real roots (i.e. √-4 = no real roots)
Negative odd power roots
-2 (i.e. ^3√-8 = -2)
Exponent radical
(-27)^2/3 = (^3√27)^2
Canceling exponents
(g+10)^5(1/5) = 70^1/5
Multiplication rule
a^m • a^n = a^m+n
5^1/2 • 5^3/2 = 5^4/2 = 5^2 = 25
Power to a power
(a^m)^n = a^m•n
(3^5/2)^2 = 3^5 = 243
Product to a power
(ab)^m = a^m•b^m
(16•9)^1/2 = 16^1/2 • 9^1/2 = 4•3 = 12
Negative exponents
a^-m = 1/a^m
36^-1/6 = 1/36^1/2 = 1/6
Quotient rule
a^m/a^n = a^m-n
4^5/2/4^1/2 = 4^4/2 = 4^2 = 16
Quotient to a power
(a/b)^m = a^m/b^m
(27/64)^1/3 = 27^1/3/64^1/3 = 3/4
Combine like terms
ax^+/-bx^m = (a+/-b)x^m
2y^1/2 - 5 ^1/2 = -3y^1/2
Operations on functions (+)
h(x) = f(x) + g(x)
Operations on functions (-)
h(x) = f(x) - g(x)
Operations on functions (x)
h(x) = f(x) x g(x)
Operations on functions (/)
h(x) = f(x)/g(x)
composition of a function
g(f(x))/f(g(x))
inverse
x = y, y = x
(1,2) (2,1)
inverse relation
a reflection of the original relation across the line y = x
inverse functions
when both the original relation and the inverse are functions
f^-1(x)
horizontal line test
the inverse of a function f is also a function if and only if no horizontal line intersects the graph of f more than once
vertical line test
the inverse of a function f is also a function if and only if no vertical line intersects the graph of f more than once
square root table
0,0 1,1 4,2
cubed root table
-1,-1 o,o 1,1
a
vertical stretch
h
translates the graph h units horizontally (x- axis) (vertical form)
k
translates the graph k units vertically (y-axis) (vertical form)
extraneous solutions
an apparent solution that must be rejected because it does not satisfy the original equation
Canceling squared roots
√x = (√x)^2
Cancel cubed root
^3√x = (^3√x)^3
Solving radical equations
GEMDAS
Solving radical equations (reminder)
factored solutions = 2 answers = cancel one of them so the original equation makes sense