# Chapter 7 (Alg 2) Flashcards

1
Q

nth root of a

A

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

2
Q

Number of Real nth Roots

A

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

3
Q

Rational Exponents

A

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

4
Q

Simplifying Variable Expressions

A

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

5
Q

A

6
Q

Extraneous solution

A

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

7
Q

Operations on Functions

A
```h(x) = f(x) + g(x)
h(x) = f(x) - g(x)
h(x) = f(x) * g(x)
h(x) = f(x) / g(x)```
8
Q

Composition of funcitons

A

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.

9
Q

Inverse relation

A

Switches input and output values

10
Q

Inverse functions

A

If the original relation and the inverse relation are functions

11
Q

Inverse functions defined

A

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

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

12
Q

Finding the inverse functions

A

switch x and y and solve for y

13
Q

Horizontal Line Test

A

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

14
Q

A

a function that has a variable in its radicand

15
Q

A

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.

16
Q

Standard Deviation

A

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)