V5(§||^ 222^ ^ J Graphing an Exponential FunctionWhat ar e t he dom ain
and range of t he
f unct io n?
Any value substituted
for/ results in a positive
y- value,The domain is
al l real numbers. The
range is all positive real
numbers.
What is the graph of y = 3 • 2 X?Make a table of x- and y-values.-2 3.2- 1 - a - J 4!)
-1 3 • 2~1 = = 1J H4)
0 3 • 2° = 3 • 1 = 3 (0, 3)(^1) 3 - 2 1 = 3 - 2 = 6 (1,6)
2 3.22 = 3- 4 = 12 (2,12)
& Got It? 3. What is the graph of each function?
a. y = 0.5 • 3X
y
ou
0
A
'<u Y
4 A “N
)
(
Jt X
0 2
Pl o t t h e p o i n t s.
Connect the points wit h a
sm o o t h cu r ve.
b. y = -0.5 • 3X
Should you connect
the points of the
g rap h?
No. The number of t i mes
you zoom in must be a
nonnegative integer.
Gr ap h in g an Ex p o n en t ial M odel
Maps Computer mapping software allows you to zoom
in on an area to view it in more detail. The function
/ ( x ) = 100 • 0.25x models the percent of the original area
the map shows after zooming in x times. Graph the function.
[•Km;
0 100-0.25° = 100 (0, 100)
1 100-0.251 = 25 (1,25)
2 100-0.252 = 6.25 (2, 6.25)
3 100-0.253 = 1.56 (3,1.56)
4100-0.254 « 0.39(4, 0.39)
1inIJUS X)
yj
:nJU
in
in_u^ :
a a1 X
0 2
& Go t It? 4. a. You can also zoom out to view a larger area on
the map. The function /(x) = 100 • 4X models
the percent of the original area the map shows
after zooming out x times. Graph the function,
b. Re aso n i n g What is the percent change in area
each time you zoom out in part (a)?
| Lesso n 7- 6 Ex p o n e n t i a l Fu n c t i o n s^455