Page 744 - Algebra 1

To graph an exponential function, make a table of ordered pairs and plot the points. The graph will always form a curve that comes close to, but never touches, the x-axis.
Graphing y = abx
Graph each function by making a table of ordered pairs.
Example
3
a. y = 5(2)x
SOLUTION
Choose both positive and negative x-values.
Caution
Due to limitations
of scale, graphs of exponential functions often appear to touch the x-axis. The graph will approach but never touch the x-axis. Since a ≠ 0 and b ≠ 0, then
y ≠ 0.
x
y
-2
1.25
-1
2.5
0
5
1
10
2
20
(-1,
2.5)
24
(1
,
_1
3)
O
O
y
(1, 1
(2, 2
x
4
0)
16
0)
(-2, 1.25)
x
-4
-2
2
b. y = -(3)x SOLUTION
Math Reasoning
Generalize Compare the domains and ranges of the functions in Examples 3a and 3b.
x
y
-1
-_1 3
0
-1
1
-3
2
-9
3
-27
-4
-2
2
4
(1, -3)
(0
, -1)
-8
-16
(2, -9)
-24
(3, -27)
_1 x c. y=6(2)
SOLUTION
x
y
-2
24
-1
12
0
6
1
3
2
1.5
(-2, 24) (-1, 12)
24
8
y
y
(0, 5)
16
(1, 3)
(0, 6)
x
O
-4
-2
2
4
(2, 1.5)
Lesson 108 729