# Chapter 8 (Alg 2) Flashcards

1
Q

Exponential function

A

y = ab^x where a DNE 0 and b>1

2
Q

Exponential growth function

A
```if a > 0, b > 1 for a Exponential Function, y grows as x increases
{}
Graph rises from left to right
graph passes through o,a and 1,ab
Domain is all real numbers
range is y > 0```
3
Q

Asymptote

A

A line that a graph approaches more and more closely

The x-axis is an asymptote of the graph of y = ab^x

4
Q

Exponential decay function

A

y = ab^x where a > 0 and 0 0

5
Q

Exponential growth, Exponential decay

A

y = a(1 + r)^t
y = a(1 - r)^t
a is the initial amount, r is the percent increase or decrease written as a decimal, t is the number of time periods

6
Q

Growth factor

A

The quantity of (1 + r)

7
Q

Decay factor

A

The quantity of (1 - r)

8
Q

Compound Interest

A

Initial principal P deposited in an account that pays interest at an annual rate r (expressed as a decimal), compounded n times per year on previously earned interest
Amount a in the account after t years can be modeled
A = P(1 + r/n)^nt

9
Q

natural base e

Euler’s number

A

irrational, defined as followed,

as n approaches + inf. (1 + 1/n)^n

10
Q

Common Logarithm

A

log with base 10 simply denoted by log

11
Q

Logarithm of y with base b

A

denoted by log base b of y
Defined as log base b of y = x if and only if
b^x = y

12
Q

Special Logarithm Values

A

Log of 1 {} log base 1 = 0

Logarithm of base b {} log base b = 1

13
Q

Inverse Functions

A
```g(f(x)) = log base b of b^x = x
f(g(x)) = b^log base b of x = x```
14
Q

Graphing logarithmic Functions

A

the graph of y = log base b of x is the reflection of the graph of y = b^x in the line y = x
The graph of y = log base b of x includes (1,0) and (b,1)
The y-axis is a vertical asymptote
The domain is x > 0, and the range is all real numbers

15
Q

To graph logs

A
```y = log base b (x - h), translate the graph of y = log base b of x horizontally h units.
y = log base b of x + h, translate the graph of y = log base b of x vertically k units```
16
Q

Change of base formula

A

let x, b, and c be positive numbers such that b DNE 1 and c DNE 1
Then, log base b of x = log base c of x over
log base c of b.
log base b of x = log of x over log of b

17
Q

Properties of Logarithms

A

Product property log base b of mn = log base b of m + log base b of n
Quotient Property log base b of m over n = log base b of m - log base b of n
Power property log base b of m^n = n of log base b of m

18
Q

Equal powers property

A

for b > 0, and b DNE 1, if b^x = b^y, then x = y

19
Q

Equal logarithms property

A

for positive numbers b, x and y where b DNE 1:

log base b of x = log base b of y if and only if x = y

20
Q

Exponentiate

A

used for when one side of the equation is in log form

For b > 0 and b DNE 1, if x = y then b^x = b^y