Logs

Front 1

logarithmic graph

Back 1

• vertical asyp at x=0

• (1,0) (#,1)

the # represents the base the log given is

Front 2

exponential graph

Back 2

•horizontal asymp at y=0

•(0,1) (1,#)

Front 3

what do these cause?:

• -x

• -function (cos, log, #)

Back 3

1. shift across y (make x int neg)

2. shift across x (make y int neg)

Front 4

log = ?

Back 4

log10

Front 5

ln(e) = ?

Back 5

1

Front 6

loga(1) = ?

Back 6

0

Front 7

loga(a) = ?

Back 7

1

Front 8

what should u remember when changing from a log to an exponential equation or vice versa?

Back 8

y = loga(x) & x = a^y

or

bae for log to e

and bao for e to log

Front 9

what are the properties of logs?

Back 9

Front 10

how do you solve absolute value equations?

Back 10

1. get rid of the absolute value brackets

2. get the absolute value on its own (if it isn't already)

3. solve like a linear equ

4. if there's more than one, you basically have to repeat steps 1-3 for the second one.

make sure once u isolate the absolute value that what comes after the = sign u make solve one for pos and one for neg

Front 11

how do you check for extraneous solutions for absolute value problems?

Back 11

plug in your answer into the original equation

Front 12

how can you tell if a function is even, odd, or neither by looking at its graph?

Back 12

even- symmetrical about the y axis

odd- symmetrical about both x and y axis

neither- ..neither lol

remember to check the coefficient to see if it's neg!!!

Front 13

degrees to radians

Back 13

multiply by the constant pi/180

Front 14

radians to degrees

Back 14

multiply by the constant 180/pi

Front 15

how do you find a coterminal angle? how do you know it's within range?

Back 15

subtract by 2pi/1 (make sure to get common den!!)

it's in range if it's less than 16pi/8

Front 16

define period. how do you find it?

Back 16

what the units are being counted by. the period is automatically 2pi. if x is being multiplied by something then u

find it by doing 2pi/1 • reciprocal of x

Front 17

define amplitude. how do you find it?

Back 17

distance from the middle of the function to the max/min height

whatever the trig function is being multiplied by is the amp

Front 18

when graphing trig functions (cos sin etc) what happens if x is being multiplied and added?

Back 18

you have to factor it to find the vertical shift.

do this by factoring out what x is being multiplied by. then we multiply whatever they gave u for pi by the recip of x)

Front 19

describe the parent function of sin

Back 19

Front 20

describe the parent function of cos

Back 20

Front 21

when do we use inverse functions?

Back 21

when we need to know an angle value

use them to isolate a trig function to get theta on its own

Front 22

when doing unit circle questions for inverse trig, what should you remember?

Back 22

u have to look at these parts of the unit circle

Front 23

what are all the fundamental identities?

Back 23

Back (Definition)

Front 24

what are the main steps for solving problems using the half and double angle formula?

Back 24

1. get equal to 0

2. use formula (note: +/- goes away as does the square and the sqrt)

3. simplify and factor to get everything being multiplied. (bc then you can solve since it's set equal to 0)

4. find answers on unit circle

Front 25

how do you solve for an angle if it's a right triangle? if it's not?

Back 25

right: plug in trig function(angle) = SOH CAH OR TOA then simplify by getting x alone.

not right: use law of sines or law of cosines

Front 26

when do you use law of sines? law of cosines?

Back 26

sine- given angles

cos- 1 or less angle or mainly sides given

u may not need to do inverse for these. the main goal is getting x alone.

Front 27

how do you graph polynomial functions?

Back 27

1. figure out if it's even or odd so u can draw the p function

2. figure out any transformations and apply. remember: fractions make u fat. if the fraction is neg, it actually gets skinner tho

Front 28

how do you find all the zeroes of a polynomial function?

Back 28

1. list all possible roots (of the first and last #)

2. use synthetic division to which root to use. u know it's the one when the remainder is 0

3. factor

Front 29

what should u remember when doing synthetic division

Back 29

above line multiply

below line add

also go down a degree when writing ur new answer

Front 30

what is tan - -1 ?

Back 30

it's not -tan. it's tan + 1

you cannot add/sub a number with a trig function

Front 31

what should u ask when adding or subtracting fractions?

Back 31

does this thing need common den

Front 32

when multiplying fractions what should u remember?

Back 32

multiply the den too

Front 33

what should u remember when dealing w problems like this?

Back 33

for the things that are boxed, do these last. solve the equ and once it's set equal to 0 u then divide or multiply the reciprocal to get rid of these.

Front 34

what can u break up in the numerator? denominator?

Back 34

num - addition

den - multiplication

Front 35

Back 35

1/x

Front 36

for rational equations, how can you determine extraneous solutions?

Back 36

set the common denominator equal to 0. those cannot be your solutions.

Front 37

case 1 for rational function graphs

Back 37

den is bigger than num

horizontal asymptote at y=0

remember the y part!!!

Front 38

case 2 for rational function graphs

Back 38

den and num are the same

divide leading coefficients to find horizontal asymptote

Front 39

case 3 for rational function graphs

Back 39

num is bigger than den

use synthetic division to figure out the slant asymptote. (make sure to change the sign!)

Front 40

what is the main goal in solving rational equations?

Back 40

get rid of the denominators and equal to 0.

get rid of den by multiplying everything by a common den

Front 41

how can you find the vertical asymptotes or holes of a rational function?

Back 41

vertical - set den equal to 0. change sign

holes - if anything cancels out, you'll have a hole there.

Front 42

what is the equation of a circle?

Back 42

(x - h)^2 + (y - k)^2 = r^2

Front 43

when dealing with square roots what should u remember?

Back 43

put the plus and minus sign!!

Front 44

unit circle

Back 44

Back (Definition)

Front 45

what's the quadratic formula

Back 45

Back (Definition)

Front 46

what happens if u get a square root that doesn't simplify?

Back 46

simplify it further by finding 2 numbers that multiply to give u that and then square root anything and put that outside and leave the one that didn't simplify inside

Front 47

when solving log equations what should u remember?

Back 47

if they have the same base u can get rid of the log

Front 48

when dealing with exponents what should u remember?

Back 48

you can only sub, add, etc if they have the same base!!

Front 49

what are the cofunction identities?

Back 49

Back (Definition)

Front 50

when should you get something equal to zero?

Back 50

when your dealing with an equation that you would need to factor. (if there's more than one trig function)

Front 51

what is (x + #)^2?

Back 51

(x + #)(x + #)

NOT X^2 + #^2

Front 52

how do you find interval of increase/decrease?

Back 52

look at x values.

remember that the function might be growing wider so it might be infinity

Front 53

what are the square root properties?

Back 53

Back (Definition)

Front 54

what's something u should remember about logs?

Back 54

u can't have negative ones

Front 55

what should u remember if a variable is on the bottom? (ie 150/b)

Back 55

multiply by the variable to get t out of the den

Front 56

how do you find the center and radius of a circle? then how do you graph it?

Back 56

center: (x - h)^2 (y - k)^2

just change the sign

radius: the # after the = sign. find what squared gives u that #.

to graph, plot ur center then ur radius tells u how many points to go out and up from there.

Front 57

how do you determine the equation of a circle?

Back 57

1. group x's and y's together

2. divide the x term by 2 the. square it. add that # to ur equ

3. subtract the # u got from step 2 from the parenthesis (to cancel it out)

4. factor

5. combine like terms and make sure it's in the equation of a circle from (add/sub the random # to the other side of the = to get the radius)

Front 58

what is the goal when solving logs?

Back 58

get x by itself.

u can do this by changing to exponential, using properties, solving like a linear equ.

Front 59

what is the goal when solving logs?

Back 59

get x by itself.

u can do this by changing to exponential, using properties, solving like a linear equ.

Front 60

how do you find plots for a rational graph?

Back 60

set x equal to 0 and y equal to 0.

Front 61

how do you find plots for a rational graph?

Back 61

set x equal to 0 and y equal to 0.

Front 62

when ur solving an equation or using the difference formulas what should you do if you get a value of a trig function that isn't on the unit circle?

Back 62

use inverse trig to get theta alone

Front 63

if ur dealing with a radian that's not on the unit circle what should u do?

Back 63

the sum/diff formula

Front 64

when looking for something on the unit circle, what should u make sure to do?

Back 64

make sure the trig function isn't neg. if it is, just divide by -1

Front 65

at the end of the test what do u need to make sure u do?

Back 65

CHECK ALL UR ANSWERS BY PLUGGING THEM BACK INTO UR ORIG EQU

Front 66

if u see something cubed, what do u need to do?

Back 66

synthetic division

Front 67

what is the domain for any polynomial?

Back 67

neg infinity to infinity or all real numbers

Front 68

what is the domain for any polynomial?

Back 68

neg infinity to infinity or all real numbers

Front 69

if ur stuck on an equ u should

Back 69

start over and start on the other side

Front 70

if u get a fraction as an answer, what should u ask?

Back 70

can i simplify this further?