Chapter 7 (Alg 2)

Question 1

nth root of a

Answer 1

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

Question 2

Number of Real nth Roots

Answer 2

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

Question 3

Rational Exponents

Answer 3

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

Question 4

Simplifying Variable Expressions

Answer 4

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

Question 5

Radical Equation

Answer 5

Contains radicals with the variable in the radicand

Question 6

Extraneous solution

Answer 6

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

Question 7

Operations on Functions

Answer 7

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

Question 8

Composition of funcitons

Answer 8

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.

Question 9

Inverse relation

Answer 9

Switches input and output values

Question 10

Inverse functions

Answer 10

If the original relation and the inverse relation are functions

Question 11

Inverse functions defined

Answer 11

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

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

Question 12

Finding the inverse functions

Answer 12

switch x and y and solve for y

Question 13

Horizontal Line Test

Answer 13

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

Question 14

Radical Function

Answer 14

a function that has a variable in its radicand

Question 15

Graphs of Radical Functions

Answer 15

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.

Question 16

Standard Deviation

Answer 16

describes the typical difference between the mean and any data value in a set.
{}
σ (sigma) = √ (x sub 1 - xbar)^2 + (x sub 2 - xbar)^2 . . .
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n
(this is all done under the√ symbol)