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Algebra 2B Credit 1
Comment:
Credit Checkpoint
Exponential Functions and Equations
ASSESSMENT Credit Checkpoint
ï‚¨ Complete the following problems. Show all your work. You will need a scientific calculator.
Learning Goal from Lesson 13.1, 13.2, and 13.3
I can determine the effect on the graph of replacing f(x) by f(x) + k, k
f(x), f(kx), and f(x + k) for specific values of k (both positive and
negative). I can determine the translation value k, given a graph for
slides, shifts, and stretches. I can explain the translation effects on the
graph of a function using technology.
How I Did (Circle one)
I got it!
Iâ€™m still learning it.
1. Which function is represented by the graph to the left? (Lesson 13.1) (1 point)
ï‚¨ A. ð‘“áˆºð‘¥áˆ» = 4ð‘¥âˆ’2 âˆ’ 3
ï‚¨ B. ð‘“áˆºð‘¥áˆ» = 4ð‘¥+2 âˆ’ 3
ï‚¨ C. ð‘“áˆºð‘¥áˆ» = 4ð‘¥âˆ’2 + 3
2. The graphs of exponential functions ð‘“ and ð‘” are shown on the coordinate plane below. (Lesson 13.1)
(1 point)
If ð‘”áˆºð‘¥áˆ» = ð‘“áˆºð‘¥áˆ» + ð‘˜, what is the value of ð‘˜?
ð‘˜ = _________________
Algebra 2B
Credit 1
L4L â€“ Algebra 2B (2020)
P a g e | 65
3. Claire buys a condo for \$350,000. The value of the condo appreciates on average 5% per year where she
bought the condo.
The value of Claireâ€™s condo, ð¶áˆºð‘¡áˆ», can be represented by which of the following functions? (Lesson 13.1)
(1 point)
ï‚¨ A. ð¶áˆºð‘¡áˆ» = 1.05ð‘¡ + 350,000
ï‚¨ B. ð¶áˆºð‘¡áˆ» = 350,000áˆº1.05áˆ»ð‘¡
ï‚¨ C. ð¶áˆºð‘¡áˆ» = 0.95ð‘¡ + 350,000
ï‚¨ D. ð¶áˆºð‘¡áˆ» = 350,000áˆº0.95áˆ»ð‘¡
4. Groundhogs are growing in a certain park based on the given function ðºáˆºð‘¡áˆ» = 30áˆº1.03áˆ»ð‘¡ , where ðºáˆºð‘¡áˆ»
represents the number of groundhogs after ð‘¡ weeks. Approximately how many weeks will there be 70
groundhogs in the park? Graph the function on a graphing calculator or at desmos.com and use the graph to
make the prediction. (Lesson 13.1) (1 point)
ï‚¨ A. After 29 weeks
ï‚¨ B. After 40 weeks
ï‚¨ C. After 237 weeks
5. A patient is taking 70 mg of a therapeutic drug. 15% of the drug is expelled from the body each hour.
Write the function that corresponds to the given situation. (Lesson 13.2) (1 point)
ð·áˆºð‘¥áˆ» = ____________________
6. Which function is represented by the graph to the left? (Lesson 13.3) (1 point)
ï‚¨ A. ð‘“áˆºð‘¥áˆ» = ð‘’ ð‘¥âˆ’1 âˆ’ 3
ï‚¨ B. ð‘“áˆºð‘¥áˆ» = ð‘’ ð‘¥+1 âˆ’ 3
ï‚¨ C. ð‘“áˆºð‘¥áˆ» = ð‘’ ð‘¥+1 + 3
Algebra 2B
Credit 1
L4L â€“ Algebra 2B (2020)
P a g e | 66
7. Which of the following describes how the function ð‘”áˆºð‘¥áˆ» = âˆ’ð‘’ ð‘¥+3 âˆ’ 4 was transformed from the graph of its
parent function ð‘“áˆºð‘¥áˆ» = ð‘’ ð‘¥ ? Select THREE that apply. (Lesson 13.3) (1 point)
ï‚¨ A. The function ð‘”áˆºð‘¥áˆ» is translated up 4 units with a horizontal asymptote of ð‘¦ = 4.
ï‚¨ B. The function ð‘”áˆºð‘¥áˆ» is translated down 4 units with a horizontal asymptote of ð‘¦ = âˆ’4.
ï‚¨ C. The function ð‘”áˆºð‘¥áˆ» is translated 3 units right.
ï‚¨ D. The function ð‘”áˆºð‘¥áˆ» is translated 3 units left.
ï‚¨ E. The function ð‘”áˆºð‘¥áˆ» is reflected across the ð‘¦ âˆ’ axis.
ï‚¨ F. The function ð‘”áˆºð‘¥áˆ» is reflected across the ð‘¥ âˆ’ axis.
Learning Goal from Lesson 13.4
I can construct exponential functions given a description of a
relationship.
How I Did (Circle one)
I got it!
Iâ€™m still learning it.
8. Jesse invests \$1250 in mutual funds with an interest rate of 9% per year. If Jesse does not withdraw any of
the money, how many years will his mutual funds be worth \$7200? Graph the function on a graphing
calculator or at desmos.com and use the graph to make the prediction. (1.5 points)
ï‚¨ A. 5.8 years
ï‚¨ B. 14.6 years
ï‚¨ C. 20.3 years
9. A principal amount of \$4200, earns 3.6% interest compounded quarterly. How long does it take for the
amount to reach 15,000? Graph the function on the calculator and use the graph to make the prediction.
(1.5 points)
ï‚¨ A. 1 year
ï‚¨ B. 3.6 years
ï‚¨ C. 23 years
ï‚¨ D. 36 years
Algebra 2B
Credit 1
L4L â€“ Algebra 2B (2020)
P a g e | 67
Learning Goal from Lesson 14.1 and 14.2
I can represent and interpret categorical and quantitative data based
on two variables (independent and dependent).
Represent means:
â€¢ I can show two-variable data on a scatter plot.
â€¢ I can describe the relationship between the variables.
â€¢ I can identify a function of best fit for the data set.
How I Did (Circle one)
I got it!
Iâ€™m still learning it.
10. The amount of bacteria in a fish tank was 830. After 5 hours, the amount of bacteria is 3202.
Complete the table to determine which of these equations could approximate the amount of bacteria.
(Lesson 14.1) (1 point)
Equation
Yes
No
ð‘ = 830áˆº1.31áˆ»â„Ž
ï‚¨
ï‚¨
ð‘ = 3202áˆº1.31áˆ»â„Ž
ï‚¨
ï‚¨
ð‘ = 830áˆº3.86áˆ»â„Ž
ï‚¨
ï‚¨
ð‘ = 3202áˆº3.86áˆ»â„Ž
ï‚¨
ï‚¨
11. Choose which sets of data can be modeled by an exponential function. (Lesson 14.1) (1 point)
Table
Yes
No
x
y
1
3
2
6
3
9
4
12
ï‚¨
ï‚¨
x
y
1
1
2
5
3
25
4
125
ï‚¨
ï‚¨
x
y
1
108
2
36
3
12
4
4
ï‚¨
ï‚¨
x
1
2
2
4
3
8
4
16
ï‚¨
ï‚¨
y
Algebra 2B
Credit 1
L4L â€“ Algebra 2B (2020)
P a g e | 68
12. Determine if a quadratic would be an appropriate model for the data shown in each scatter plot. Select two
that apply. (Lesson 14.2) (1 point)
Graphs
Algebra 2B
Yes
No
ï‚¨
ï‚¨
ï‚¨
ï‚¨
ï‚¨
ï‚¨
ï‚¨
ï‚¨
Credit 1
L4L â€“ Algebra 2B (2020)
P a g e | 69
13. You and your friend are working on a group project. Your partner did all the mathematical calculations on a
graphing calculator. It is now your turn to complete Parts 2 and 4 below to draw conclusions based on
The table below shows the total attendance at major league baseball games, at 10-year intervals since
1930. Use the table for the problems that follow. Round all answers to the nearest thousandth.
Major League Baseball Total Attendance (y), in millions,
in years since 1930 (x)
x
0
10
20
30
40
50
60
70
80
y
10.1
9.8
17.5
19.9
28.7
43.0
54.8
72.6
73.1
Part 1: Use a graphing calculator to find the linear regression, quadratic regression, and exponential
regression for the data. Then graph all three models.
ð‘¦ = 0.897ð‘¥ + 0.738
Part 2:
y = 0.007x 2 + 0.304x + 7.654
y = 11.504 âˆ™ 1.025x
Which model is a good fit for the data? Explain by comparing the three graphs. (1 point)
___________________________________________________________________________________________________________________________
___________________________________________________________________________________________________________________________
Part 3:
Use each regression model to predict major league baseball attendance for year 2020.
Linear:
Exponential:
81.5 ð‘šð‘–ð‘™ð‘™ð‘–ð‘œð‘› in attendance
91.7 ð‘šð‘–ð‘™ð‘™ð‘–ð‘œð‘› in attendance
120.4 ð‘šð‘–ð‘™ð‘™ð‘–ð‘œð‘› in attendance
Part 4: Which prediction seems the most likely? Explain by comparing the three predicted baseball
attendances. How can you accurately know which regression model is the best fit? (1 point)
____________________________________________________________________________________________________________________________
____________________________________________________________________________________________________________________________
Checkpoint
Score
15
Algebra 2B
Credit 1
L4L â€“ Algebra 2B (2020)
P a g e | 70
Updated 10/12/2021
Algebra 2B
Credit 1
L4L â€“ Algebra 2B (2020)
P a g e |8
Algebra 2B
Credit 1
Exponential Functions and Equations
Credit Goals
â€¢ In this credit, students will:
o transform function graphs of exponential functions.
o construct and differentiate linear and exponential functions, including arithmetic and geometric
sequences.
o model exponential and other functions by fitting the function to the data.
In this credit, you will learn about exponential functions. This page summarizes all the key features of exponential
functions that you will learn in each lesson.
Key Features of exponential functions with base b: ð’‡áˆºð’™áˆ» = ð’‚ âˆ™ ð’ƒð’™
Exponential functions with base e: ð’‡áˆºð’™áˆ» = ð’†ð’™
Exponential functions in investments: ð‘¨áˆºð’•áˆ»
Algebra 2B
Credit 1
L4L â€“ Algebra 2B (2020)
P a g e |9
Lesson 13.1 Exponential Growth Functions
Learning Goal: I can determine the effect on the graph of replacing
f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both
positive and negative). I can determine the translation value k, given
a graph for slides, shifts, and stretches. I can explain the translation
effects on the graph of a function using technology.
(Standard F-BF.B.3)
EXPLORE
L4L Math Resource Center
http://Bit.ly/L4LMath
Graphing and Analyzing ð’‡áˆºð’™áˆ» = ðŸð’™ and ð’‡áˆºð’™áˆ» = ðŸðŸŽð’™
ï‚¨ Read Explore Parts A-F and complete the following activity (adapted from Lesson 13.1).
Algebra 2B
Credit 1
L4L â€“ Algebra 2B (2020)
P a g e | 10
Graphing Combined Transformations of ð’‡áˆºð’™áˆ» = ð’ƒð’™
Where ð’ƒ > ðŸ
EXPLAIN 1
ï‚¨ Read Explain 1 Parts A and B and complete Your Turn #1 â€“ 3 (adapted from Lesson 13.1).
A given exponential function ð‘”áˆºð‘¥áˆ» = ð‘Ž(ð‘ ð‘¥âˆ’â„Ž ) + ð‘˜ with base ð‘ can be graphed by recognizing the differences
between the given function and its parent function, ð‘“áˆºð‘¥áˆ» = ð‘ ð‘¥ . The following define the parameters of the
transformation:
Transformations for the Exponential Function ð’ˆáˆºð’™áˆ» = ð’‚(ð’ƒð’™âˆ’ð’‰ ) + ð’Œ
The impact of ð’‚ on ð’ƒð’™
Vertical
Reflection
Vertical
Stretch
â†’
When ð‘Ž is negative
â†’
When |ð‘Ž| is greater
than 1
Vertical
Compression
â†’
When |ð‘Ž| is between
0 and 1
Example 1
The impact of ð’‰ on ð’ƒð’™
Shift
Right
Shift
Left
â†’
â†’
When â„Ž is
positive
When â„Ž is
negative
The impact of ð’Œ on ð’ƒð’™
Shift
Up
Shift
Down
â†’
â†’
When ð‘˜ is
positive
When ð‘˜ is
negative
Compare the graphs of ð’ˆáˆºð’™áˆ» to their parent function ð’‡áˆºð’™áˆ». State the transformations that
have been performed on ð’ˆáˆºð’™áˆ» from the parent function ð’‡áˆºð’™áˆ».
A. ð‘”áˆºð‘¥áˆ» = âˆ’3áˆº2ð‘¥âˆ’2 áˆ» ; ð‘“áˆºð‘¥áˆ» = 2ð‘¥
âˆ’3áˆº2ð‘¥âˆ’2 áˆ» compared to 2ð‘¥
ð‘Ž = âˆ’3
Compare and contrast the difference between ð‘”áˆºð‘¥áˆ» and ð‘“áˆºð‘¥áˆ».
Observe the value of a
Reflect across the ð‘¥ âˆ’axis
âˆ’3 is a negative
Vertical stretch by a factor of 3
Since |âˆ’3| > 1
â„Ž=2
Translate 2 units right
Observe the value of â„Ž
Since â„Ž is positive
The transformations that have been performed on ð’ˆáˆºð’™áˆ» are a reflection across the ð’™ âˆ’ axis,
vertical stretch by a factor of ðŸ‘, and translate ðŸ units right.
1
B. ð‘”áˆºð‘¥áˆ» = 2 áˆº10ð‘¥ áˆ» + 1 ; ð‘“áˆºð‘¥áˆ» = 10ð‘¥
1
áˆº10ð‘¥ áˆ» + 1 compared to 10ð‘¥
2
1
2
1
Vertical compression by a factor of 2
ð‘Ž=
ð‘˜=1
Translate 1 unit up
Compare and contrast the difference between ð‘”áˆºð‘¥áˆ» and ð‘“áˆºð‘¥áˆ».
Observe the value of ð‘Ž
1
Since |2| < 1 Observe the value of ð‘˜ Since ð‘˜ is positive The transformations that have been performed on ð’ˆáˆºð’™áˆ» are a vertical compression by a ðŸ factor of ðŸ and translate ðŸ unit up. Algebra 2B Credit 1 L4L â€“ Algebra 2B (2020) P a g e | 11 Your Turn Compare the graphs of ð’ˆáˆºð’™áˆ» to their parent function ð’‡áˆºð’™áˆ». State the transformations that have been performed on ð’ˆáˆºð’™áˆ» from the parent function ð’‡áˆºð’™áˆ». 1. ð‘”áˆºð‘¥áˆ» = 4áˆº2ð‘¥+2 áˆ» âˆ’ 6 ; ð‘“áˆºð‘¥áˆ» = 2ð‘¥ 3 2. ð‘”áˆºð‘¥áˆ» = âˆ’ 5 áˆº10ð‘¥âˆ’4 áˆ» + 3 ; ð‘“áˆºð‘¥áˆ» = 10ð‘¥ 1 3. Compare the graph of ð‘”áˆºð‘¥áˆ» = 2 áˆº2áˆ» ð‘¥âˆ’1 + 3 with the graph of ð‘“áˆºð‘¥áˆ» = 2ð‘¥ . Which statement is true? ï‚¨ A. ð‘”áˆºð‘¥áˆ» is vertically stretched by a factor of 2. ï‚¨ B. ð‘”áˆºð‘¥áˆ» is translated up 3 units. ï‚¨ C. ð‘”áˆºð‘¥áˆ» is reflected across the ð‘¦-axis. Algebra 2B Credit 1 L4L â€“ Algebra 2B (2020) P a g e | 12 Writing Equations for Combined Transformations of ð’‡áˆºð’™áˆ» = ð’ƒð’™ Where ð’ƒ > ðŸ
EXPLAIN 2
ï‚¨ Read Explain 2 Parts A and B and complete Your Turn #1 (adapted from Lesson 13.1).
Given the graph of an exponential function, the function rule for the graph is created by using the knowledge
of the transformation parameters.
From the exponential function ð‘“áˆºð‘¥áˆ» = ð‘ ð‘¥ , there are two reference points:
1. áˆº0, 1áˆ»
2. áˆº1, ð‘áˆ»
In the transformation from ð‘”áˆºð‘¥áˆ» = ð‘Ž(ð‘ ð‘¥âˆ’â„Ž ) + ð‘˜, the point áˆº0, 1áˆ» becomes áˆºâ„Ž, ð‘Ž + ð‘˜áˆ» and áˆº1, ð‘áˆ» becomes
áˆº1 + â„Ž, ð‘Žð‘ + ð‘˜áˆ».
The asymptote ð‘¦ = 0 for the parent function ð‘“áˆºð‘¥áˆ» = ð‘ ð‘¥ becomes ð‘¦ = ð‘˜ for the exponential function
ð‘”áˆºð‘¥áˆ» = ð‘Ž(ð‘ ð‘¥âˆ’â„Ž ) + ð‘˜.
Key Features
Parent Function
Transformation Function
ð‘>1
ð‘“áˆºð‘¥áˆ» = ð‘ ð‘¥
ð‘”áˆºð‘¥áˆ» = ð‘Ž(ð‘ ð‘¥âˆ’â„Ž ) + ð‘˜
First reference point
áˆº0, 1áˆ»
áˆºâ„Ž, ð‘Ž + ð‘˜áˆ»
Second reference point
áˆº1, ð‘áˆ»
áˆº1 + â„Ž, ð‘Žð‘ + ð‘˜áˆ»
Asymptote
ð‘¦=0
ð‘¦=ð‘˜
Example 2 Write the exponential function that is represented by the graph given using the parent
function ð’‡áˆºð’™áˆ».
A. Parent function ð‘“áˆºð‘¥áˆ» = 5ð‘¥
Since ð‘“áˆºð‘¥áˆ» = 5ð‘¥ , ð‘ = 5.
The asymptote is ð‘¦ = âˆ’5, showing that ð‘˜ = âˆ’5.
The first reference point is áˆº1, âˆ’4áˆ». This shows
that â„Ž = 1 and that ð‘Ž + ð‘˜ = âˆ’4.
Substitute ð‘˜ = âˆ’5 and solve for ð‘Ž.
ð‘Ž + ð‘˜ = âˆ’4
ð‘Ž âˆ’ 5 = âˆ’4
ð‘Ž=1
Therefore, ð‘Ž = 1, ð‘ = 5, â„Ž = 1 and ð‘˜ = âˆ’4
Substitute these values into ð‘”áˆºð‘¥áˆ» = ð‘Ž(ð‘ ð‘¥âˆ’â„Ž ) + ð‘˜.
ð’ˆáˆºð’™áˆ» = (ðŸ“ð’™âˆ’ðŸ ) âˆ’ ðŸ“
Algebra 2B
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B. Parent function ð‘“áˆºð‘¥áˆ» = 2ð‘¥
Since ð‘“áˆºð‘¥áˆ» = 2ð‘¥ , ð‘ = 2.
The asymptote is ð‘¦ = 3, showing that ð‘˜ = 3.
The first reference point is áˆºâˆ’1, 1áˆ». This shows
that â„Ž = âˆ’1 and that ð‘Ž + ð‘˜ = 1.
Substitute ð‘˜ = 3 and solve for ð‘Ž.
ð‘Ž+ð‘˜ = 1
ð‘Ž+3=1
ð‘Ž = âˆ’2
ð‘=2
â„Ž = âˆ’1
ð‘˜=3
Substitute these values into ð‘”áˆºð‘¥áˆ» = ð‘Ž(ð‘ ð‘¥âˆ’â„Ž ) + ð‘˜.
ð’ˆáˆºð’™áˆ» = âˆ’ðŸ(ðŸð’™+ðŸ ) + ðŸ‘
Write the exponential function that is represented by the graph given using the parent function ð’‡áˆºð’™áˆ».
1. Parent function ð‘“áˆºð‘¥áˆ» = 4ð‘¥
Algebra 2B
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EXPLAIN 3
Modeling with Exponential Growth Functions
An exponential growth function has the form ð´áˆºð‘¡áˆ» = ð‘ƒáˆº1 + ð‘Ÿáˆ»ð‘¡ where ð‘ƒ is the initial value and ð‘Ÿ is a
constant percent increase for each unit of time ð‘¡.
Example 3
Find the function that corresponds with the given situation. Then use the graph of the
function to make a prediction.
A. Tony purchased a rare guitar in 2,000 for \$12,000. Experts estimate that its value will increase by 14%
per year. In how many years will the guitar be worth \$60,000? Graph the function on a graphing
calculator or at desmos.com and use the graph to make the prediction.
Step 1 – Find the exponential growth function ð‘¨áˆºð’•áˆ» that represents the value of Tonyâ€™s guitar
ð‘ƒ = 12000
ð‘Ÿ = .14
Tony purchased the guitar for \$12,000.
The increase in value is 14%. Must be converted to a decimal before substituting.
Substitute the values for ð´áˆºð‘¡áˆ».
ð´áˆºð‘¡áˆ» = ð‘ƒáˆº1 + ð‘Ÿáˆ»ð‘¡
ð´áˆºð‘¡áˆ» = 12000áˆº1 + .14áˆ»ð‘¡
ð´áˆºð‘¡áˆ» = 12000áˆº1.14áˆ»ð‘¡
Step 2 â€“ Use the graph of the function to make a prediction
Since the question is when will the guitar be worth \$60,000, ð´áˆºð‘¡áˆ» = 60000.
Find the value of ð‘¡ by graphing the following functions on a graphing calculator or at desmos.com/calculator.
ð´áˆºð‘¡áˆ» = 12000áˆº1.14áˆ»ð‘¡
ð´áˆºð‘¡áˆ» = 60000
The two functions are shown to cross at áˆº12.283, 60000áˆ» meaning ð‘¡ = 12.283.
Thus, Tonyâ€™s guitar is worth \$ðŸ”ðŸŽ, ðŸŽðŸŽðŸŽ after about 12 years.
Find the function that corresponds with the given situation. Then use the graph of the function to make a
prediction.
1. John researches a baseball card and finds that it is currently worth \$3.25. However, it is supposed to
increase in value 11% per year. In how many years will the card be worth \$26. Graph the function on a
graphing calculator or at desmos.com and use the graph to make the prediction.
Algebra 2B
Credit 1
L4L â€“ Algebra 2B (2020)
P a g e | 15
Learning Goal from Lesson 13.1
I can determine the effect on the graph of replacing f(x) by f(x) +
k, k f(x), f(kx), and f(x + k) for specific values of k (both positive
and negative). I can determine the translation value k, given a
graph for slides, shifts, and stretches. I can explain the translation
effects on the graph of a function using technology.
Lesson Reflection (Circle one)
Startingâ€¦
Getting thereâ€¦
Got it!
Lesson 13.1 Checkpoint
ï¯ Once you have completed the above problems and checked your solutions, complete the Lesson Checkpoint
below.
ï¯ Complete the Lesson Reflection above circling your current understanding of the Learning Goal.
1. Compare the graph of ð‘”áˆºð‘¥áˆ» = âˆ’5áˆº2áˆ» ð‘¥+1 with the graph ð‘“áˆºð‘¥áˆ» = 2ð‘¥ .
State the transformations that have been performed on ð‘”áˆºð‘¥áˆ» from the parent function ð‘“áˆºð‘¥áˆ».
2. Which function is represented by the graph to the
left?
3. The graphs of exponential functions ð‘“ and ð‘” are
shown on the coordinate plane below.
ï‚¨ A. ð‘“áˆºð‘¥áˆ» = âˆ’2ð‘¥+1 âˆ’ 3
If ð‘”áˆºð‘¥áˆ» = ð‘“áˆºð‘¥ âˆ’ ð‘˜áˆ», what is the value of ð‘˜?
ï‚¨ B. ð‘“áˆºð‘¥áˆ» = âˆ’2ð‘¥+1 + 3
ð‘˜ = ___________
ï‚¨ C. ð‘“áˆºð‘¥áˆ» = âˆ’2ð‘¥âˆ’1 + 3
Algebra 2B
Credit 1
L4L â€“ Algebra 2B (2020)
P a g e | 18
Lesson 13.2 Exponential Decay Functions
Learning Goal: I can determine the effect on the graph of replacing
f(x) by f(x) + k, k f(x), f(kx), and f(x + k) for specific values of k (both
positive and negative). I can determine the translation value k, given
a graph for slides, shifts, and stretches. I can explain the translation
effects on the graph of a function using technology.
(Standard F-BF.B.3)
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ðŸ ð’™
ðŸ
ð’™
Graphing and Analyzing ð’‡áˆºð’™áˆ» = (ðŸ) and ð’‡áˆºð’™áˆ» = (ðŸðŸŽ)
ï‚¨ Read Explore Parts A-H and complete the following activity (adapted from Lesson 13.2).
Algebra 2B
Credit 1
L4L â€“ Algebra 2B (2020)
P a g e | 19
Graphing Combined Transformations of ð’‡áˆºð’™áˆ» = ð’ƒð’™
Where ðŸŽ < ð’ƒ < ðŸ EXPLAIN 1 ï‚¨ Read Explain 1 Parts A and B and complete Your Turn #1-2 (adapted from Lesson 13.2). Example 1 Compare the graphs of ð’ˆáˆºð’™áˆ» to their parent function ð’‡áˆºð’™áˆ». State the transformations that have been performed on ð’ˆáˆºð’™áˆ» from the parent function ð’‡áˆºð’™áˆ». 1 ð‘¥âˆ’6 A. ð‘”áˆºð‘¥áˆ» = 5 (2) 1 ð‘¥âˆ’6 5 (2) 1 ð‘¥ + 2 ; ð‘“áˆºð‘¥áˆ» = (2) 1 ð‘¥ + 2 compared to (2) ð‘Ž=5 Vertical stretch by a factor of 5 â„Ž=6 Translate 6 units right ð‘˜=2 Translate 2 units up Compare and contrast the difference between ð‘”áˆºð‘¥áˆ» and ð‘“áˆºð‘¥áˆ». Observe the value of ð‘Ž Since |5| > 1
Observe the value of â„Ž
Since â„Ž is positive
Observe the value of ð‘˜
Since ð‘˜ is positive
The transformations that have been performed on ð’ˆáˆºð’™áˆ» are a vertical stretch by a factor of 5,
translate ðŸ” units right and translate ðŸ units up.
Algebra 2B
Credit 1
L4L â€“ Algebra 2B (2020)
P a g e | 20
1 1 ð‘¥
1 ð‘¥
B. ð‘”áˆºð‘¥áˆ» = 4 (5) âˆ’ 7 ; ð‘“áˆºð‘¥áˆ» = (5)
1 1 ð‘¥
1 ð‘¥
( ) âˆ’ 7 compared to (5)
4 5
Compare and contrast the difference between ð‘”áˆºð‘¥áˆ» and ð‘“áˆºð‘¥áˆ».
1
4
1
Vertical compression by a factor of 4
Observe the value of ð‘Ž
ð‘Ž=
1
Since |4| < 1 ð‘˜ = âˆ’7 Observe the value of ð‘˜ Translate 7 unit down Since ð‘˜ is negative The transformations that have been performed on ð’ˆáˆºð’™áˆ» are a vertical compression by ðŸ a factor of ðŸ’ and translate ðŸ• unit down. Your Turn Compare the graphs of ð’ˆáˆºð’™áˆ» to their parent function ð’‡áˆºð’™áˆ». State the transformations that have been performed on ð’ˆáˆºð’™áˆ» from the parent function ð’‡áˆºð’™áˆ». 1 ð‘¥+2 1. ð‘”áˆºð‘¥áˆ» = 3 (3) 1ð‘¥ âˆ’ 4 ; ð‘“áˆºð‘¥áˆ» = 3 1 ð‘¥+1 2. Compare the graph of ð‘”áˆºð‘¥áˆ» = (5) Which statement is true? 1 ð‘¥ âˆ’ 1.5 with the graph of ð‘“áˆºð‘¥áˆ» = (5) . 1 ï‚¨ A. ð‘”áˆºð‘¥áˆ» is compressed by a factor of 5. ï‚¨ B. ð‘”áˆºð‘¥áˆ» is translated up 1.5 units. ï‚¨ C. ð‘”áˆºð‘¥áˆ» is translated left 1 unit. Algebra 2B Credit 1 L4L â€“ Algebra 2B (2020) P a g e | 21 Writing Equations for Combined Transformations of ð’‡áˆºð’™áˆ» = ð’ƒð’™ Where ðŸŽ < ð’ƒ < ðŸ EXPLAIN 2 ï‚¨ Read Explain 2 Part A and complete Your Turn #1-2 (adapted from Lesson 13.2). Given the graph of an exponential function, the function rule for the graph is created by using the knowledge of the transformation parameters. From the exponential function ð‘“áˆºð‘¥áˆ» = ð‘ ð‘¥ , there are two reference points: 1. áˆº0, 1áˆ» 1 2. (âˆ’1, ð‘) 1 In the transformation from ð‘”áˆºð‘¥áˆ» = ð‘Ž(ð‘ ð‘¥âˆ’â„Ž ) + ð‘˜, the point áˆº0, 1áˆ» becomes áˆºâ„Ž, ð‘Ž + ð‘˜áˆ» and (âˆ’1, ð‘) becomes ð‘Ž (â„Ž âˆ’ 1, ð‘ + ð‘˜). The asymptote ð‘¦ = 0 for the parent function ð‘“áˆºð‘¥áˆ» = ð‘ ð‘¥ becomes ð‘¦ = ð‘˜ for the exponential function ð‘”áˆºð‘¥áˆ» = ð‘Ž(ð‘ ð‘¥âˆ’â„Ž ) + ð‘˜. Key Features 0 Purchase answer to see full attachment

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