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Level 408

Exponential & Logarithmic Functions


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Base
the number that is written with an exponent
exponent
A mathematical notation indicating the number of times a quantity is multiplied by itself
power
a number produced by raising a base to an exponent
Domain
The ______________________ is all the possible INPUT, X, values.
Range
The difference between the greatest number and the least number in a set of data.
Exponential Function
y = ab^x
logarithmic function
the inverse of the exponential function
common logarithms
The logarithm with base 10 is called the common logarithm and is denoted by omitting the base
log
abbreviation of common logarithms
natural logarithms
logarithmic functions of base e
e
Eulers number.
increasing function
a function whose graph increases as the values of the domain increase
decreasing functions
a function whose graph decreases as the values of the domain increase
constant function
a functions whose graph stays horizontal as the values of the domain increase
y-intercept
the point where the line crosses the y-axis
inverse relation
the relation that reverses each ordered pair (a,b) to (b,a)
one to one function
a function that has an inverse that is also a function
Horizontal Line Test
inverse of a function is also a function if and only if no horizontal line intersects more than one
log(b)1
0
log(b)b
1
log(b)b^x
x
b^log(b)x
x
log1
0
log10
1
log10^x
x
10^logx
x
ln1
0
lne
1
lne^x
x
e^lnx
x
log(b)N+log(b)M
The Product Rule: log(b)(MN)
log(b)N-log(b)M
The Quotient Rule: log(b)(M/N)
plog(b)M
The Power Rule: log(b)M^p
logM/logb
Change of Base (common logs): log(b)M
lnM/lnb
Change of Base (natural logs): log(b)M
F(x)=b^x
The exponential function with base b
f(x)=e^x
(Steeper Exponential Growth)
A=P(1+r/n)^(nt)
Formula for interest compounded n times per year
A=Pe^(rt)
Investment total under continuously compounded interest; A=...
log(b)x=y
Express in logarithmic form: y=b^x
y=b^x
Express in exponential form: log(b)x=y
e
An irrational number called the natural base
Describe the transformation f(x)=b^(x)+c
Shifts the graph c units upward
Describe the transformation f(x)=b^(x)-c
Shifts the graph c units downward
Describe the transformation f(x)=-b^x
Reflects the graph about the x-axis
Describe the transformation f(x)=b^(-x)
Reflects the graph about the y-axis
Vertical Stretch c>1
Describe the transformation f(x)=cb^x