Ch. 6 Test

Question 1

Domain and Range of exponential functions

Answer 1

The domain will always be (-∞,∞)
The range will be (asymptote, ∞)

Question 2

The asymptote of an exponential function

Answer 2

Usually, y=0 unless there is a transformation on the outside of the x
then the asymptote will be that number

Question 3

Compound interest growth formula

Answer 3

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

Question 4

What does r stand for

Answer 4

Rate (percent)
When the rate is inside parentheses, move decimal over 2

Question 4

What does n stand for

Answer 4

Times per yer

Question 4

What does t stand for

Answer 4

Amount of years

Question 4

Compound interest decay formula

Answer 4

A= p(1-percent decrease with decimal moved)^t

Question 5

Continuous compound interest formula

Answer 5

A= P(e)^r(move decimal)t

Question 5

When an exponential graph has a shift up or down, what changes?

Answer 5

The asymptote

Question 5

When simplifying an expression, the answer will always be x unless there is a…

Answer 5

1 or zero

Question 5

When simplifying an expression, the answer will always be x unless it is an…

Answer 5

e function with a number in front of the base, then it will be 1

Question 6

How to find the inverse of exponential functions

Answer 6

Switch x and y
convert to log form

Question 7

How to find the inverse of log functions

Answer 7

switch x and y
convert to exponential form

Question 8

How to find the inverse of the ln form

Answer 8

Switch x and y
Convert to e form using e^x=ln
get y by itself

Question 9

How to find the inverse of e form

Answer 9

switch x and y
Convert to ln form using e= lnx
get rid of the x and make ln x equal the power
get y by itself

Question 10

How to graph log functions

Answer 10

Convert to exponential form and make a table
Switch x and y on the table and plot points

Question 11

Domain and range of log functions

Answer 11

The domain will be (asymptote,∞)
The range will always be (-∞, ∞)

Question 12

The asymptote of a log function

Answer 12

Usually, x=0 unless there is a transformation on the inside of the x (moving it left or right)
then the asymptote will be that number

Question 13

What does a vertical stretch do to a point on a graph?

Answer 13

Multiplies the y-value by that number

Question 14

What does a horizontal stretch do to a point on a graph?

Answer 14

Multiplies the x-value by that number

Question 15

When you add two logs with the same base, what happens?

Answer 15

They get multiplied

Question 16

Subtract two logs with the same base, what happens?

Answer 16

They get divided

Question 17

If part of a log function (the x of the log function) has an exponent, where does the exponent go?

Answer 17

In front of the log
Loga U^n -> n Log a U

Question 18

Change of base

Answer 18

Loga b -> Log b/Log a

Question 19

Log 10 =

Answer 19

1

Question 20

What do you do when expanding/condensing, if there is a root?

Answer 20

Get rid of the root and write as a fraction

Question 21

How to solve equations in exponential form

Answer 21

Make bases the same (whatever you take out/add must be applied to the exponent)
Once bases are the same, they will cancel and the exponents will be left
Solve for x

Question 22

How to solve equations in log form

Answer 22

Make sure the bases are the same and they will cancel out

Question 23

How to solve e equations

Answer 23

get e^x by itself
Put ln in front of both sides
The ln e^x will cancel and leave the exponent by itself
Solve for x and plug into calculator

Question 24

What do you do when you have two log functions on the same side of an equation?

Answer 24

Condense them
Change the number on the other side to the log’s base to the power of that number
Solve

Question 25

What do you do when you have two ln functions on the same side of an equation?

Answer 25

Condense them
Change the number on the other side to e to the power of that number
Solve

Question 26

How to convert two points to an exponential function

Answer 26

Write two equations using y=ab