Intermediate Algebra (11th edition)

CHAPTER 10 Summary 623

10.1

one-to-one function
inverse of a function

10.2

exponential function
asymptote
exponential equation

10.3

logarithm

logarithmic equation

logarithmic function

with base a

10.5

common logarithm

natural logarithm

universal constant

10.6

compound interest

continuous compounding

KEY TERMS

the inverse of

the logarithm of x

with base a

loga x

ƒ^11 x 2 ƒ 1 x 2 log x common (base 10)
logarithm of x

ln x natural (base e)

logarithm of x

e a constant,

approximately

2.718281828

NEW SYMBOLS

1.In a one-to-one function
A.each x-value corresponds to only
one y-value
B.each x-value corresponds to one
or more y-values
C.each x-value is the same as each
y-value
D.each x-value corresponds to only
one y-value and each y-value
corresponds to only one x-value.

2.If ƒ is a one-to-one function, then
the inverseof ƒ is
A.the set of all solutions of ƒ
B.the set of all ordered pairs formed
by interchanging the coordinates
of the ordered pairs of ƒ
C.the set of all ordered pairs that
are the opposite (negative) of the
coordinates of the ordered pairs
of ƒ

D.an equation involving an

exponential expression.

3.An exponential functionis a

function defined by an expression

of the form

A. for real

numbers a, b, c

B. for positive

numbers aand x

C. for all real numbers x

D. for

4.An asymptoteis

A.a line that a graph intersects just

once

B.a line that the graph of a function

more and more closely

approaches as the x-values

increase or decrease

ƒ 1 x 2 = 2 x xÚ0.

1 a 7 0, aZ 12

ƒ 1 x 2 =ax

1 aZ 12

ƒ 1 x 2 =loga x

1 aZ 02

ƒ 1 x 2 =ax^2 +bx+c

C.the x-axis or y-axis

D.a line about which a graph is

symmetric.

5.A logarithmis

A.an exponent

B.a base

C.an equation

D.a polynomial.

6.A logarithmic functionis a

function that is defined by an

expression of the form

A. for real

numbers a, b, c

B. for positive

numbers aand x

C. for all real numbers x

D.ƒ 1 x 2 = 2 xfor xÚ0.

1 a 7 0, aZ 12

ƒ 1 x 2 =ax

1 aZ 12

ƒ 1 x 2 =loga x

1 aZ 02

ƒ 1 x 2 =ax^2 +bx+c

TEST YOUR WORD POWER

See how well you have learned the vocabulary in this chapter.

SUMMARY

CHAPTER 10

ANSWERS
1.D; Example:The function is one-to-one. 2.B; Example:The inverse of the one-to-one function ƒ
defined in Answer 1 is 3.C; Examples: 4.B; Example:
The graph of has the x-axis as an asymptote. 5.A; Example: is the exponent to which amust be raised to obtain x;
log 3 9 = 2 since 32 =9. 6.B; Examples: y=log 3 x, y=log1/3 x

ƒ 1 x 2 = 2 x 1 y= 02 loga x

ƒ 1 x 2 = 4 x, g 1 x 2 =A 21 B h 1 x 2 = 2 - x+^3

x

ƒ -^1 = 51 2, 0 2 , 1 - 1, 1 2 , 1 5, 3 2 , 1 3, - 226. ,

ƒ= 51 0, 2 2 , 1 1, - 12 , 1 3, 5 2 , 1 - 2, 3 26