Test 4

Question 1

Determine if function is one to one

Answer 1

1. 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
2. Horizontal line test

Question 2

determine if the two functions are inverses of each other

Answer 2

plug them into each other and they should both simplify to just x

Question 3

Find the inverses of each function that is one to know given a set of ordered pairs

Answer 3

1. All x’s have to be different

2. Switch X and Y values for inverse

Question 4

Find the inverse of the equation

Answer 4

1. Look at graph first to see if its 1:1
2. Switch X and Y and solve for Y
3. f^-1(x)

Question 5

Inverse or not from graph

Answer 5

Find points, should be switched of each other

Question 6

Facts to remember about inverses

Answer 6

1. If its 1:1 it has an inverse
2. Domain and range are switched in inverse
3. Graphs are reflections across y=x, so if (a,b) is on graph f, then (b,a) is on graph f^-1
4. To find the equation for f-1, switch x and y, solve for y, and replace with f-1(x)

Question 7

given f equation and x inequality

Answer 7

1. find the inverse equation
2. replace x with y
3. graph

Question 8

Exponential function graphs if a>1

Answer 8

1. Increasing and continuos over (-infinity, infinity)
2. x-axis is the horizontal asymptote
3. points (-1, 1/a), (0,1), (1,a)
4. Up to the right

Question 9

Exponential function graphs if 0<a></a>

Answer 9

1. decreasing and continuos over (-infinity, infinity)
2. x-axis is asymptote
3. points (-1, 1/a), (0,1), (1,a)
4. up to the left, down to the right

Question 10

solving equations exponenets

Answer 10

1. make base the same and set exponents equal
2. if just variable, multiply exponent by reciprocal
3. making exponent negative gets rid of fraction
4. making exponent fraction gets rid of root
5. ln to get rid of e- can divide out

Question 11

compounded a specific amount of time

Answer 11

A= P (1 + r/n)^nt

Question 12

compounded continuously

Answer 12

A=Pe^rt

Question 13

log circle

Answer 13

LogaX=y, a^y=x

Question 14

switch exponent from negative to positive

Answer 14

take what it equals to and make it the reciprocal

Question 15

log graph if a>1

Answer 15

1. increasing continuously over (0, infinity)
2. y-axis is vertical asymptote
3. Points (1/a, -1), (1,0), (a,1)
4. up to the right
5. a is little number

Question 16

log graph if a is between 0 and 1

Answer 16

1. flipped over x axis

2. same but down to the right

Question 17

asymptote with translation

Answer 17

moves also

Question 18

Loga1

Answer 18

0

Question 19

Logaa

Answer 19

1

Question 20

LogaXY

Answer 20

logaX + logaY

Question 21

Loga x/y

Answer 21

logaX - logaY

Question 22

logaX^r

Answer 22

rlogaX

Question 23

a^loga^x

Answer 23

X

Question 24

logaa^x

Answer 24

x

Question 25

how to simplify logs with x and y on top and bottom

Answer 25

subtract exponents and if negative, move to the bottom

Question 26

log10X

Answer 26

LogX=common log

Question 27

LnX

Answer 27

logeX=natural log

Question 28

find decibels given Io

Answer 28

plug in top and cancel out units, given calculator problem

Question 29

solving exponential equations when you can't make a common base

Answer 29

1. Make both coefficients have a log with the base of the smaller number so Logaa=1 2. Left with a calculator problem on other side 3. If exponent, becomes major because your putting it in front of (1)

Question 30

e

Answer 30

ln both sides, cancels out e

Question 31

before you ln

Answer 31

simplify as much as possible

Question 32

can divide out if

Answer 32

on both sides

Question 33

Lne=

Answer 33

1

Question 34

exponential growth formula same as

Answer 34

compounded continuously

Question 35

find when something will tripe

Answer 35

1. 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

Question 36

doubling time formula

Answer 36

t= ln2/r

Question 37

doubling rate formula

Answer 37

r= ln2/t