Pre-calculus
Name__________________________________
Review #3 Chapter 4 Exponential and Logarithmic Functions
Mrs. Spatola
Pre-calculus 2009
In this chapter, you will be able to:
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Determine Whether a Function is One-to-One
Obtain the Graph of the Inverse Function from the Graph of the Function
Find an Inverse Function
Evaluate Exponential Functions
Define the Number e
Change Exponential Expressions to Logarithmic Expressions
Change Logarithmic Expressions to Exponential Expressions
Evaluate Logarithmic Functions
Determine the Domain of a Logarithmic Function
Graph Logarithmic Functions
Write a Logarithmic Expression as a Sum/Difference of Logarithms
Write a Logarithmic Expression as a Single Logarithm
Evaluate Logarithms Whose Base Is Neither 10 nor e
Graph Logarithmic Functions Whose Base is Neither 10 nor e
Solve Logarithmic Equations
Solve Exponential Equations
1. Determine whether the function is one-to-one.
2. Decide whether or not the functions are inverses of each other.
f(x) = 4x - 2, g(x) =
3. a) Find the inverse of f(x) = 2x + 3
b) Find the inverse of f ( x) 
2x  1
x 1

4) Verify that f(x) = 2x + 3 and f (x) = ½(x - 3) are inverses of each other
5) The graph of a one-to-one function is given. Draw the graph of the inverse
function f-1. For convenience, the graph of y = x is also given.
6) The function f is one-to-one. State the domain and the range of f and f-1. f(x) =
Domain: f(x) ____________________________ Range: f(x) _________________________
Domain f-1(x) ____________________________ Range: f-1(x) _______________________
7) Define the number e and give its approximate numerical value.
8) State the domain and range, x-intercepts; y-intercept, asymptote(s) :
a) f(x) = ax, a > 1
b) f(x) = ax, 0 < a < 1
9) Determine whether the given function is exponential or not. If it is exponential, identify the value of
the base a.
10) Determine the exponential function whose graph is given.
f(x) = ________________
11) Change the exponential expression to an equivalent expression involving a logarithm.
a)
72 = 49
b)
ex = 6
12) Change the logarithmic expression to an equivalent expression involving an exponent.
a) log3
b) ln
= -3
= -2
13) Find the domain of the Log Function
a) f(x) = log2(1 – x)
b) g(x) = log5(
1 x
)
1 x
x 2  1 ) as a sum of logarithms. Express all powers as factors.
14) a) Write log a(x
x2
b) Write log a(
) as a difference of logarithms. Express all powers as factors.
( x  1) 3
c) Write log a(
x3 x2  1
) as a difference of logarithms. Express all powers as factors.
( x  1) 4
15) Condense the logarithmic expression.
a)
loga7 + 4loga3
c)
2ln(x+2) - lnx
b)
1
log x  3 log ( x  1)
10
2 10
16) Evaluating logarithms whose base is neither 10 or e.
a) Evaluate log107
c) Evaluate log
2
b) Evaluate log589
5
17) Solving Simple Exponential and Logarithmic Equations
a) 2 x  32
b) log 10 x  1
c) log 3 (4 x  7)  2
d) 2 log 5 x  log 5 9
f) 3 x  1  81
e) log 4 ( x  3)  log 4 (2  x)  1
g) 5 x  2  33x  2
h) e x +
i) loga(x-1) – loga(x+6) = loga(x-2)-loga(x-3)
3
= πx
18) Fill in the blank.
a) If every horizontal line intersects the graph of a function f at no more than one point,
then f is a(n) _______________________________________function.
b) If f--1 denotes the inverse of a function f, then the graphs of f and f -1 are symmetric with
respect to the line ____________________________________.
c) The graph of every exponential function f(x) = ax , a > 0, a ≠ 1, passes through the two
points __________________________________.
d) The logarithm of a product equals the ____________________________ of the logarithms.
e) For every base, the logarithms of _____________________________equals 0.
f) The domain of the logarithmic function f(x) = loga x consists of ______________________.
g) The graph of every logarithmic function f(x) = loga x, a > 0, a ≠ 1, passes through the two
points _____________________________________.