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Name ________________________________________ Date __________________ Class __________________
LESSON
12-2
Geometric Sequences
Practice and Problem Solving: A/B
Each rule represents a geometric sequence. If the given rule is
recursive, write it as an explicit rule. If the rule is explicit, write it as
a recursive rule. Assume that f(1) is the first term of the sequence.
1. f(n) = 11(2)n−1
2. f(1) = 2.5; f(n) = f(n − 1) i 3.5 for n ≥ 2
________________________________________
3. f(1) = 27; f(n) = f(n − 1) i
________________________________________
1
for n ≥ 2
3
4. f(n) = −4(0.5)n−1
________________________________________
________________________________________
Write an explicit rule for each geometric sequence based on the given
terms from the sequence. Assume that the common ratio r is positive.
5. a1 = 90 and a2 = 360
6. a1 = 16 and a3 = 4
________________________________________
________________________________________
7. a1 = 2 and a5 = 162
8. a2 = 30 and a3 = 10
________________________________________
________________________________________
9. a4 = 135 and a5 = 405
10. a3 = 400 and a5 = 256
________________________________________
________________________________________
11. a2 = 80 and a5 = 10
12. a4 = 22 and a7 = 0.022
________________________________________
________________________________________
A bank account earns a constant rate of interest each month.
The account was opened on March 1 with $18,000 in it. On April 1,
the balance in the account was $18,045. Use this information
for Problems 13–15.
13. Write an explicit rule and a recursive rule that can be used to find A(n),
the balance after n months.
_________________________________________________________________________________________
14. Find the balance after 5 months.
_________________________________________________________________________________________
15. Find the balance after 5 years.
_________________________________________________________________________________________
Original content Copyright © by Houghton Mifflin Harcourt. Additions and changes to the original content are the responsibility of the instructor.
187
Graphing Exponential Functions
Name
Period #
x
Ex 1: The function y = 3 is called an _____________________________ function because the exponent is a
____________________________.
Now, let’s look at how to graph the exponential function
x
-3
y = 3x
1
1
y = 3( −3) = 3 =
27
3
y
y = 3x .
(x, y)
-2
-1
0
1
2
3
Definition 1: Since the y values increase as the x values increase in the example above, this is what we call
exponential ___________________________. (The graph goes up the hill from left to right)
QUESTION: In the exponential function
y = 3 x , the y-values can never equal or be less than ____________.
Definition 2: Since the y-value can NEVER equal zero in this function, there is a horizontal
__________________________ at y = 0.
Ex 2: By looking at the graph above, list the domain and range of the function
DOMAIN:
RANGE:
y = 3x
x
⎛1⎞
Ex 3: Now, let’s look at how to graph the exponential function y = ⎜ ⎟ .
⎝3⎠
⎛1⎞
y =⎜ ⎟
⎝3⎠
x
x
y
(x, y)
-3
-2
-1
0
1
2
3
Definition 3: Since the y values decrease as the x values increase in the example above, this is what we call
exponential ___________________________. (The graph goes down the hill from left to right)
QUESTION: Is there an asymptote? If so, where is it?
⎛1⎞
Ex 4: By looking at the graph above, list the domain and range of the function y = ⎜ ⎟
⎝3⎠
x
DOMAIN:
RANGE:
Tell whether the functions below show exponential GROWTH or DECAY.
⎛1⎞
5) y = ⎜ ⎟
⎝4⎠
8)
y =5
x
x
6)
y = 2x
9)
x
y=0
7)
y =1x
⎛2⎞
10) y = ⎜ ⎟
⎝3⎠
x
Graphing Exponential Functions Practice Worksheet
Name
Period #
Graph the following functions and tell whether they show exponential growth or decay.
1)
x
y = 2x
y
(x, y)
-3
-2
-1
0
1
2
3
Does the function above show exponential GROWTH or DECAY?
2)
x
⎛1⎞
y =⎜ ⎟
⎝2⎠
x
y
(x, y)
-3
-2
-1
0
1
2
3
Does the function above show exponential GROWTH or DECAY?
3)
y = 1x
x
y
(x, y)
-3
-2
-1
0
1
2
3
Does the function above show exponential GROWTH or DECAY?
Tell whether the functions below show exponential GROWTH or DECAY.
4)
y=9
x
⎛2⎞
7) y = ⎜ ⎟
⎝7⎠
x
⎛1⎞
5) y = ⎜ ⎟
⎝5⎠
x
⎛5⎞
8) y = ⎜ ⎟
⎝6⎠
x
6)
y = 4x
9)
y = 0x
Algebra 1
Unit: Exponential Functions
Homework
Name
Date
Hour
Graphing Exponential Functions Worksheet #2
Directions​: Answer all questions. Show all work!!!
Sketch the graph of each function. Then, state the Domain, Range, and
Y-intercept, and change of Y-values of the function.
1. y = 8 • ( 12 ) x
X
Y
-1
0
1
2
3
4
5
6
Domain:
Range:
Y-Intercept: (
,
)
Change in Y-Values:
Growth or Decay? ​____________
1
7
2
2. y =
• 2x
X
Y
-4
-3
-2
-1
0
1
2
3
4
Domain:
Range:
Y-Intercept: (
,
)
Change in Y-Values:
Growth or Decay? ​____________
2
x
3. y =− 6 • ( 12 )
X
Y
-2
-1
0
1
2
3
4
5
6
7
Domain:
Range:
Y-Intercept: (
,
)
Change in Y-Values:
Growth or Decay? ​____________
3
4. y = 0.5 x
X
Y
-3
-2
-1
0
1
2
3
Domain:
Range:
Y-Intercept: (
,
)
Change in Y-Values (b) :
Growth or Decay? ​____________
4

Kuta Software - Infinite Algebra 1
Name___________________________________
Exponential Functions
Date________________ Period____
Evaluate each function at the given value.

1) f ( x) =  x at x

2) f (n) =  n at n
3) f (n) =  n at n
 
4) g( x) = 
 
x

6) f ( x)

x
()
at x
Sketch the graph of each function.
5) f ( x) x




()
y

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

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
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

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






y

x
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Worksheet by Kuta Software LLC


7) f ( x)  x

8) f ( x)





()
x
y


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


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
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



x

y




x
Write an equation for each graph.
9)




10)
y






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

x
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
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Worksheet by Kuta Software LLC