2.71828
2-’
e’ from Figures 13 and 15(a) and reflect about
Graph the function
ye would have to go for the height of the
graph of
xample demonstrates the rapid growth of this func
surprise you.
(d)v= e—l
in Figure 15(b). (Notice that the graph crosses the
Dompress the graph vertically by a factor of 2 to
15(c). Finally, we shift the graph downward one
15(d). The domain is ll and the range is (—I, cc).
=
I exponential function
d range.
D.r
V
atural exponential function.
e
cimal places, is
r
”’
3
x
.
(b)
(h)
4
)
3
(6v
(b) x(3x
3
)
2
(b)
=
9. y
3’,
e’,
v
=
=
v
v
io’,
=
=
(k)’,
8’,
v
v
()
8’
=
=
v=5’,v =20’
e’,
e’.
Graphing calculator or computer wiih graphing software required
=
8. v
7.v=2.v
7—10 Graph the given functions on a common screen. How are
these graphs related?
6. (a) How is the number e defined?
(b) What is an approximate value for e?
(c) What is the natural exponential function?
5. (a) Write an equation that defines the exponential function
with base a > 0.
(b) What is the domain of this function?
(c) If a
1, what is the range of this function?
(d) Sketch the general shape of the graph of the exponential
function for each of the following cases.
(i) a > 1
(ii) a = I
(iii) 0 < a < I
4. (a)
”
2
x
3. (a) 4
(2b)
8
b
2. (a) 8’
1. (a)
expression.
1—4 Use the Law of Exponents to rewrite and simplify the
1 Exercises
FIGURE 16
=
0.9’.v
ylO’
0.6’,
v
0.3’,
15
y
=
0.1’
Y
=
=
=
1
—
e’
—2’
l02
y
V
16. y
14.
12.
=
=
2(1
—
(0.5)’
2
e)
—
=
sin(e’)
l—e
‘
1. Homework Hints available in TEC
20. (a) g(t)
19.(a)fc)=
(b) g(t)
=
/l
—
2’
(b)f(x)
e
19—20 Find the domain of each tunction.
18. Starting with the graph of v
e, find the equation of the
graph that results from
(a) reflecting about the line v = 4
(b) reflecting about the line x = 2
17. Starting with the graph of v
e ‘, write the equation of the
graph that results from
(a) shifting 2 units downward
(b) shifting 2 units to the right
(c) reflecting about the x-axis
(d) reflecting about the y-axis
(e) reflecting about the x-axis and then about the y-axis
15. y
13. v
11.
11—16 Make a rough sketch of the graph of the function. Do not
use a calculator. Just use the graphs given in Figures 3 and 13
and, if necessary, the transformations of Section 1.3.
10. v
0
1.5 X lO