Unit 2 B

Question 1

log function general form

Answer 1

f(x)=alog(b)x
a does not = 0
b > 0

Question 2

domain of general log function

Answer 2

(0, inf)
cannot take the log of a negative number

Question 3

range of general log function

Answer 3

(-inf, +inf)
like a square root

Question 4

if a > 0 and b >1

Answer 4

cd, growth

Question 5

VA of reg log

Answer 5

x = 0

Question 6

if a < 0 and b > 1

Answer 6

reflection over x axis
cu, decay

Question 7

increasing vs. decreasing

Answer 7

only one!
no relative extrema unless on a closed interval

Question 8

cu vs. cd

Answer 8

only one!
no points of inflection

Question 9

end behavior limit statements of a log

Answer 9

left as x –> 0 (+/-)
right as x –> inf

Question 10

logs in table

Answer 10

x values change proportionally

Question 11

product property of logs

Answer 11

log(b)xy = log(b)x + log(b)y

Question 12

quotient property of logs

Answer 12

log(b)x/y = log(b)x - log(b)y

Question 13

power property of logs

Answer 13

log(b)x^m = m*log(b)x

Question 14

to use power rules of logs…

Answer 14

bases (b) must be the same

Question 15

b^log(b)c =

Answer 15

c

Question 16

log(b)b^a =

Answer 16

a

Question 17

change of base property of logs

Answer 17

log(b)a = log(c)a/log(c)b

Question 18

natural logarithm function

Answer 18

lnx

Question 19

lnx =

Answer 19

log(e)x

Question 20

log graph

Answer 20

(
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|
|

Question 21

product property of exponents

Answer 21

b^m*b^n=b^(m+n)

Question 22

power property of exponents

Answer 22

(b^m)^n=b^m*n

Question 23

negative exponent property

Answer 23

b^-n=1/b^n

Question 24

if logs have the same base and are set equal to each other…

Answer 24

can cancel log

Question 25

when solving logs, remember to…

Answer 25

check for extraneous solutions!
- negative number
- zero

Question 26

log of a proper fraction

Answer 26

negative

Question 27

equations with multiple exponential functions

Answer 27

find common bases using the properties of exponents

Question 28

if the bases of exponential functions are the same

Answer 28

cancel base and set exponents equal to eachother

Question 29

quadratic formula

Answer 29

[-b+/-(sqrt : b^2-4ac)]/2a

Question 30

general form of exponential

Answer 30

f(x) = ab^(x+h)+k

Question 31

general form of log

Answer 31

f(x)=alog(b)(x+h)+k

Question 32

when finding inverses make sure to..

Answer 32

use correct inverse notation!

Question 33

solving logarithmic inequalities

Answer 33

combine log
change forms
undo fraction
move to one side
factor
put zeros and undefined values on sign chart
test points

Question 34

in a semi-log plot

Answer 34

y axis is logarithmically scaled
exponential functions will appear lineasr

Question 35

linear equation for semi log plot

Answer 35

y = logbx+loga
slope : logb
y-int : loga
base = the base of the vertical axis

Question 36

f(g(x)) is the same as

Answer 36

fog(x)

Question 37

inverse graph

Answer 37

reflection over y=x

Question 38

inverses if…

Answer 38

f(g(x))=x & g(f(x))=x

Question 39

exponential is just…

Answer 39

logarithmic rewritten

Question 40

b^c=a

Answer 40

log(b)a=c

Question 41

log table

Answer 41

ex. but switched
x changes proportionally

Question 42

if f(x)=b^x and g(x)=log(b)x

Answer 42

they are inverses

Question 43

log(b)b^a=

Answer 43

a

Question 44

log form

Answer 44

f(x) = alog(b)x

Question 45

b^log(b)c=

Answer 45

c