Test 4 Flashcards
Determine if function is one to one
- set the number side of equation equal to itself replacing x with a and b on either side. If a=b it is one to one
- Horizontal line test
determine if the two functions are inverses of each other
plug them into each other and they should both simplify to just x
Find the inverses of each function that is one to know given a set of ordered pairs
- All x’s have to be different
2. Switch X and Y values for inverse
Find the inverse of the equation
- Look at graph first to see if its 1:1
- Switch X and Y and solve for Y
- f^-1(x)
Inverse or not from graph
Find points, should be switched of each other
Facts to remember about inverses
- If its 1:1 it has an inverse
- Domain and range are switched in inverse
- Graphs are reflections across y=x, so if (a,b) is on graph f, then (b,a) is on graph f^-1
- To find the equation for f-1, switch x and y, solve for y, and replace with f-1(x)
given f equation and x inequality
- find the inverse equation
- replace x with y
- graph
Exponential function graphs if a>1
- Increasing and continuos over (-infinity, infinity)
- x-axis is the horizontal asymptote
- points (-1, 1/a), (0,1), (1,a)
- Up to the right
Exponential function graphs if 0<a></a>
- decreasing and continuos over (-infinity, infinity)
- x-axis is asymptote
- points (-1, 1/a), (0,1), (1,a)
- up to the left, down to the right
solving equations exponenets
- make base the same and set exponents equal
- if just variable, multiply exponent by reciprocal
- making exponent negative gets rid of fraction
- making exponent fraction gets rid of root
- ln to get rid of e- can divide out
compounded a specific amount of time
A= P (1 + r/n)^nt
compounded continuously
A=Pe^rt
log circle
LogaX=y, a^y=x
switch exponent from negative to positive
take what it equals to and make it the reciprocal
log graph if a>1
- increasing continuously over (0, infinity)
- y-axis is vertical asymptote
- Points (1/a, -1), (1,0), (a,1)
- up to the right
- a is little number
log graph if a is between 0 and 1
- flipped over x axis
2. same but down to the right
asymptote with translation
moves also
Loga1
0
Logaa
1
LogaXY
logaX + logaY
Loga x/y
logaX - logaY
logaX^r
rlogaX
a^loga^x
X
logaa^x
x
how to simplify logs with x and y on top and bottom
subtract exponents and if negative, move to the bottom
log10X
LogX=common log
LnX
logeX=natural log
find decibels given Io
plug in top and cancel out units, given calculator problem
solving exponential equations when you can’t make a common base
- Make both coefficients have a log with the base of the smaller number so Logaa=1
- Left with a calculator problem on other side
- If exponent, becomes major because your putting it in front of (1)
e
ln both sides, cancels out e
before you ln
simplify as much as possible
can divide out if
on both sides
Lne=
1
exponential growth formula same as
compounded continuously
find when something will tripe
- find rate first with given information
2. Use the same value for Yo (a) but change Y to triple of given value, actual given value is not used
doubling time formula
t= ln2/r
doubling rate formula
r= ln2/t
