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
