Chapter 3 Review

Exponential Functions and Graphs:

functions:

f(x) = a^x , where a>0 and a cannot equal 0

*every exponential graph : have a horizontal asymptote @ Y=0

: has a y-intercept of 1

: no x-intercept

: domain is all read numbers (-∞, ∞)

: range of (0, ∞)

y = ab^(x-c) + d

a- causesthe graph to vertically stretch or shrink and changes y-intercept

c- causes the graph to move left or right where left moves positive and right moves more negative
d- causes the graph to move up and down

b- how fast, if less than 1 there is decay

x- a negative x causes the graph to reflect in the y-axis

Properties of Exponents:

a^x * a^y = a^(x+y)
a^x / a^y = a^(x-y)
a^-x = 1 / a^x

The Natural Base e:

f(x) = e^x
Domain: (-∞, ∞)
Range: (0, ∞)
y-intercept: (0,1)

Compound Interest:
Continuously Compounded Interest: A = Pe^rt
A = present value
P = principle value (how much invested)
r = annual rate of return (decimal form)
t = time in years

*r and t must be some time frame, the units of time must agree

Discretely Compounded Interest: A = P(1 + r/n)^nt
n = number of compounding periods per year

Logarithmic Functions

common log-

log10= log

natural log-

loge= ln

*** key to everything ***

log a x = y <--> a^y = x

log 2 16 = 4 <--> 2^4= 16

Log Graphs:

Domain: (0, ∞)

Range: (-∞, ∞)
x-intercept: (0,1)

V.A.: x=0

Transformation is log graphs:

y = alogb (x-c) + d

a= stretches graph, neg. reflects in x-axis

b= growth rate, less than 1 decrease in graph

c= moves right or left

d= moves up or down

Properties of Logs:

Summary of Exponential and Logarithmic Functions: