Ch. 6 Test Flashcards
Domain and Range of exponential functions
The domain will always be (-∞,∞)
The range will be (asymptote, ∞)
The asymptote of an exponential function
Usually, y=0 unless there is a transformation on the outside of the x
then the asymptote will be that number
Compound interest growth formula
A= p(1+r/n)^nt
What does r stand for
Rate (percent)
When the rate is inside parentheses, move decimal over 2
What does n stand for
Times per yer
What does t stand for
Amount of years
Compound interest decay formula
A= p(1-percent decrease with decimal moved)^t
Continuous compound interest formula
A= P(e)^r(move decimal)t
When an exponential graph has a shift up or down, what changes?
The asymptote
When simplifying an expression, the answer will always be x unless there is a…
1 or zero
When simplifying an expression, the answer will always be x unless it is an…
e function with a number in front of the base, then it will be 1
How to find the inverse of exponential functions
Switch x and y
convert to log form
How to find the inverse of log functions
switch x and y
convert to exponential form
How to find the inverse of the ln form
Switch x and y
Convert to e form using e^x=ln
get y by itself
How to find the inverse of e form
switch x and y
Convert to ln form using e= lnx
get rid of the x and make ln x equal the power
get y by itself
How to graph log functions
Convert to exponential form and make a table
Switch x and y on the table and plot points
Domain and range of log functions
The domain will be (asymptote,∞)
The range will always be (-∞, ∞)
The asymptote of a log function
Usually, x=0 unless there is a transformation on the inside of the x (moving it left or right)
then the asymptote will be that number
What does a vertical stretch do to a point on a graph?
Multiplies the y-value by that number
What does a horizontal stretch do to a point on a graph?
Multiplies the x-value by that number
When you add two logs with the same base, what happens?
They get multiplied
Subtract two logs with the same base, what happens?
They get divided
If part of a log function (the x of the log function) has an exponent, where does the exponent go?
In front of the log
Loga U^n -> n Log a U
Change of base
Loga b -> Log b/Log a
Log 10 =
1
What do you do when expanding/condensing, if there is a root?
Get rid of the root and write as a fraction
How to solve equations in exponential form
Make bases the same (whatever you take out/add must be applied to the exponent)
Once bases are the same, they will cancel and the exponents will be left
Solve for x
How to solve equations in log form
Make sure the bases are the same and they will cancel out
How to solve e equations
get e^x by itself
Put ln in front of both sides
The ln e^x will cancel and leave the exponent by itself
Solve for x and plug into calculator
What do you do when you have two log functions on the same side of an equation?
Condense them
Change the number on the other side to the log’s base to the power of that number
Solve
What do you do when you have two ln functions on the same side of an equation?
Condense them
Change the number on the other side to e to the power of that number
Solve
How to convert two points to an exponential function
Write two equations using y=ab
