=
25
—(In 24
In 2
—
In 5)
56.58 years
y
=
-v
—
I.
—
—
—
ot y In v as given in Figure 13. Using the
transfor
nlx
1
rty
)
2
units to the right to get the graph of y
In(x
2)
lb get the graph of y = 1n(x
2)
I. (See Fig
1
g
iiithm lunctjon
logarithmic functions with base greater than 1, the natural
on defined on (0, x and the y-axis is a vertical asymptote.
otlnx become very large negative as x approaches 0.)
=
al function y = e’ and its inverse function, the natural loga
Figure 13. Because the curve y = er crosses the y-axis with
te reflected curve y = Ins crosses the s-axis with a slope of I.
Natural Logarithm
graphical estimate that we made in Example 3(c) in
‘(5)
--
0.49
0
FIGURE 15
0
4.
3.
3
5.3
4
2.8
5
2.0
6
1.9183.53.119
2.0
J
Graphing calculator or computer with graphing software required
1.0
1.5
1Cr)
3
1
x
2
3—14 A function is given by a table of values, a graph, a formula, or
a verbal description. Determine whether it is one-to-one.
2. (a) Suppose f is a one-to-one function with domain A and
range B. How is the inverse function jI defined? What is
the domain of f’? What is the range of f?
(b) If you are given a formula for f, how do you find a
formula forf?
(c) If you are given the graph off, how do you find the graph
off ‘?
1. (a) What is a one-to-one function?
(b) How can you tell from the graph of a function whether it is
one-to-one?
rnircises
1.41
0.69
2
1
0
1
0.72
2.24
1.61
5
0.73
3.16
2.30
10
g(s)
=
=
I/s
2
.v
—
2x
0.28
12. q(s)
=
=
—
V
3x
/
x
Computer algebra system required
14. f(t) is your height at age t.
0.04
1. Homework Hints available in TEC
,
7/
woo
0.09
coss
10
11.5
100,000
100 f316
9.2
10,000
—
10. f(s)
8.
6.
0.22
7
22.4f
6.2J9
500j 1000
13. f(r) is the height of a football t seconds after kickoff.
11.
FIGURE 16
0
0.46
0.55
4.6
10.0
-
100
7.07
3.91
50
\c>
9. f(s)
7.
5.
1=1n.v
—--
lnx
x