PRACTICE
Match each equation to its original graph. Then match it to the graph of its inverse.
1
2
𝑦=
____ ____
ORIGINAL
INVERSE
PRACTICE
3
𝑦 = log 𝑥
𝑦 = log
____ ____
____ ____
ORIGINAL
INVERSE
ORIGINAL
A
4
.
𝑥
INVERSE
B
C
D
𝑦=2
____ ____
ORIGINAL
INVERSE
Consider the functions in the box at right.
A
𝑦=
(5) Sketch a graph of each function on the axes provided.
(6) Which functions are inverses of one another? _____
AND
_____
(7) Which function have a horizontal asymptote? _____
AND
_____
B
𝑦 = log 𝑥
(8) Which function has a range of all real numbers? _____
(9) Which function represents a decreasing exponential function? _____
(10) Which functions have a domain of all real numbers? _____
PRACTICE
Consider the exponential equation 𝑦 = 10
AND
C
𝑦=5
_____
+ 3.
(11) Sketch a graph of the function.
(12) Where is the function’s asymptote? ___________
(13) Sketch an approximate graph of the function’s inverse.
(14) Where is the asymptote of the inverse? ___________
(15) How is your answer to #14 related to what you know about inverses?
PRACTICE
_____________________________
Circle the equation that represents the asymptote of each graph.
(16) The asymptote of 𝑦 = log(𝑥 − 3) + 4 is…
(17) The asymptote of 𝑦 = log(𝑥) − 2 is…
a) 𝑦 = 3
a) 𝑥 = 0
b) 𝑥 = 3
c) 𝑦 = 4
d) 𝑥 = 4
b) 𝑦 = 0
c) 𝑥 = −2
d) 𝑦 = −2
(18) The asymptote of 𝑦 = log(𝑥 + 7) is…
(19) The asymptote of 𝑦 = log(𝑥) + 7 is…
a) 𝑦 = 0
a) 𝑦 = 0
PRACTICE
b) 𝑥 = 0
c) 𝑥 = −7
d) 𝑦 = −7
b) 𝑥 = 0
c) 𝑥 = −7
d) 𝑦 = −7
(20) Write the equation of the asymptote of the graph of 𝑦 = log(𝑥 + 5) − 9. __________
Solve each equation.
REVIEW
(21) log (3𝑥 + 1) = 2
(22) log (3𝑥 + 2) = 5
x=____
(23) log(𝑥 + 3) = 2
x=____
(24) log (𝑥 ) = 4 x=____
(26) log ((𝑥 − 1) ) = 4
(25) log(𝑥 − 3𝑥) = 1
x=____ ____
x=____ ____
x=____ ____
REVIEW
Mr. Whistlethistle is preparing his will, and plans on leaving money in separate bank
accounts for his three children, Bill, Jill, and Phil. Into Bill’s account is deposited $30,000, but the
account will not gain interest. Into Jill’s account is deposited $15,000, and the account will gain 4%
annual interest compounded continuously. Into Phil’s account is deposited $12,000, and the account
will gain 4% annual interest compounded quarterly.
(27) Write an expression to represent
the value of each child’s account.
_____________
_____________
BILL
JILL
_____________
PHIL
(28) If Mr. Whistlethisle dies in 20 years, which child’s account will be the most valuable? __________
PROVE IT:
Evaluate each expression.
REVIEW
(29) log 256 _____
(30) log
a)
b)
(
_____
)
(𝑥) =_____________
(40) If 𝑓(𝑥) = −5,
what is the value of x? ______
(32) log
8 _____
.
c)
d)
Consider the functions 𝑓(𝑥) = log 𝑥 , 𝑔(𝑥) = 𝑥 , ℎ(𝑥) = 𝑥 − 𝑥
(34) 𝑓 𝑘(16) =________
(37) 𝑓
(31) log
(33) Select the expression that is equivalent to
REVIEW
REVIEW
1 _____
and 𝑘(𝑥) = √𝑥.
(35) 𝑘 𝑓(1) =________
(36) ℎ 𝑔(1) =________
(38) ℎ 𝑘(𝑥) =_____________
(39) 𝑘 ℎ(𝑥) =_____________
(41) If ℎ(𝑥) = 0, then x=______
(42) If 𝑓 𝑔(𝑥) = 4,
what is the value of x? ______
x=______, or x=______