Honors Algebra II
5.1 – Exponential Functions and Their Graphs
Name:
Warm Up: Can you solve the following equations? Round to the nearest 1000th’s when necessary.
I
1) 2!"#$ = 8
2) 3" = 15
2211 I
x 1
8
8
2
x 2
2212
1
8
8
3
32 9
33 2
8
5
15.58
32 3
12.5
4 2.46497
a 465
If the annual rate of inflation averages 4% over the next 20 years, the approximate cost C of goods or services
during any year in the following 2 decades will be modeled by C(t) = P(1.04)t, where t is the time in years
and P is the present cost. The current cost of an oil change for your car is $23.95.
C 23.95 1.04
a) Fill out the following table for C(t) and quickly graph your results
t
C(t)
0
23.95
24.91
29.14
1
5
10
20
It
100
4
60
cost so
yo
35.457
30
52.48 Y
To
Ismet
yrs
b) Is C(t) linear? That is, is there a common slope/rate between each of the points from the table? If the
function holds true for many years to come, identify C(45).
I
No
c) Identify each of the following from the table of C(t):
1) domain:
0,20
, )
023
2) range: 23.95
52.48 3) y-int: (
II. Exponential Functions and technology:
a) Using your graphing calculator, graph the following function: f(x) = 3-x
1) domain:
C 00,00
2) range:
o ooo
3) y-int: (
,
)
4) asymptote:
4 0
III. f(x) has a horizontal asymptote at the line y = 0. Mathematically speaking, why is this?
3
1
1
x
x
3
3
I
3
20
130
o
T
20
IV. Circle the term that accurately completes each statement.
g
O
a) C(t) is an example of exponential growth/decay while f(x) is an example of exponential growth/decay.
III. Exponential Functions and Transformations:
f
a) Graph g(x) = 2x on your graphing calculator and identify each of the following:
o
1) domain:
2) range:
C00,00
o
3) y-int: (O ,
)
4) asymptote:
4 0
o
b) Graph a second equation (Y2 ) as h(x) = 2x + 3 – 5 on your graphing calculator and identify each of the
following:
left
3
1) domain:
10
2) range:
3) y-int: ( 03
, )
4) asymptote:
4 5
Alg
15,00
c) Which value from h(x) caused the horizontal shift? With the sign or opposite the sign?
C00,00
x 3
left 3
opp sign
d) Which value from h(x) caused the vertical shift? With the sign or opposite the sign?
5
down 5
w
sign
1
e) What type of transformation would occur from f(x) to h(x) if f(x) = 4x -2 + 1 and h(x) = -(4x -2 + 1) ?
Reflection over x axis
9 4
Iggy
y