# Chapter 7 (Alg 2) Flashcards

nth root of a

nth rt. a where a is a real number and n is the index of the radical, the index is the n

Number of Real nth Roots

n>1 and a is a real number {} if n is odd, and a is any real number, then the number of nth roots of a is 1

if n is even and a is greater than 0, then the number of nth roots of a is two, if a is zero, the number of nth roots of a is one, if a is less than zero, the number of nth roots is none

Rational Exponents

Let a^1/n be an nth root of a (a>0 and a DNE 1), and let ma be a positive integer.

{}

a^m/n = (a^1/n)^m = (nth root of a)^m

a^-m/n = 1/a^m/n = 1/(a^1/n)^m = 1/(nth root of a)^m

Simplifying Variable Expressions

nth root x^n = x when n is odd; nth root x^n = |x| when n is even

Radical Equation

Contains radicals with the variable in the radicand

Extraneous solution

Raising each side of an equation to the same power can lead to solutions that do not make the original equation true. An apparent solution that does not make the original equation true is an Extraneous solution

Operations on Functions

h(x) = f(x) + g(x) h(x) = f(x) - g(x) h(x) = f(x) * g(x) h(x) = f(x) / g(x)

Composition of funcitons

h(x) = f(g(x))

The domain of h is the set of all x-values where x is in the domain of g and g(x) is in the domain of f.

Inverse relation

Switches input and output values

Inverse functions

If the original relation and the inverse relation are functions

Inverse functions defined

f(g(x)) = x ; g(f(x)) = x

Denoted by f^-1 (not read as f to the neg. first power)

Finding the inverse functions

switch x and y and solve for y

Horizontal Line Test

if a graph is intercepted by a hor. line, it doesn’t have an inverse function

Radical Function

a function that has a variable in its radicand

Graphs of Radical Functions

To graph, y = a(Sqrt.x-h) + k, sketch graph of y = a sqrt. x or y = a 3rdrt. x

if h is neg. translate left, opp. for positive

in k is pos. translate up, opp. for neg.