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| Section | Objectives |
|---|---|
| Exponential Functions | - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions |
| Logistic Functions | - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions |
| Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on graphs - Derive conclusions based on notation |
| Validity of Models | - Examine utility - Determine fit - Determine validity |
| Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Graphical Depictions | - Interpret inputs and outputs for situations - Interpret asymptotes for situations - Interpret rates of change for situations - Interpret concavity for situations - Interpret maximum and minimum for situations |
| Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions |
Question 1
The graph shows the weekly profit in hundreds of dollars for a coffee shop. The horizontal axis represents the number of years since the coffee shop opened.
What is the correct interpretation of the minimum value?
A. Approximately 13 years after opening, a minimum weekly profit of approximately $4,630was earned.
B. Approximately 6 years after opening, a minimum weekly profit of approximately $990was earned.
C. Approximately 13 years after opening, a minimum weekly profit of approximately $990was earned.
D. Approximately 6 years after opening, a minimum weekly profit of approximately $4,630was earned.
Question 2
The logistic function f(x), whose graph is shown, models the number of people with a viral infection, where x represents the number of days since the outbreak of the virus and f(x) represents the number of viral infections.
What happens as time progresses from day 9 to day 12?
A. The number of people with the virus decreases faster and faster.
B. The number of people with the virus increases faster and faster.
C. The number of people with the virus decreases slower and slower.
D. The number of people with the virus increases slower and slower.
Question 3
The number of tasks completed by computer B is 12 more than the number of tasks completed by computer A. Let F(x)represent the relationship between the number of tasks completed by the two computers, where xis the number of tasks completed by computer A and Fis the number of tasks completed by computer B.
Which function represents this situation?
A. F(x)=x+12
B. F(x)=x-12
C. F(x)=x/12
D. F(x)=12x
Question 4
The exponential function
f(x)=280× # 1.08 # ^x
represents the number of subscribers to a blog, where xrepresents the number of years since 2003 and f(x) represents the number of subscribers.
Which statement correctly interprets the average rate of change of the number of subscribers from 2003 to
2007? Round to the nearest whole number, if necessary.
A. The number of subscribers decreases at an average rate of 330 subscribers per year.
B. The number of subscribers decreases at an average rate of 25 subscribers per year.
C. The number of subscribers increases at an average rate of 25 subscribers per year.
D. The number of subscribers increases at an average rate of 330 subscribers per year.
Question 5
A contractor charges a flat rate plus a fixed rate per hour to come and make repairs. For a job that takes 3 hours, the contractor charges $220. For a job that takes 5 hours, the contractor charges $340.
Which function correctly represents the total charge Cfor a job that takes thours?
A. C(t)=40t
B. C(t)=60t+40
C. C(t)=40t+60
D. C(t)=60t
Solutions:
| Question 1 Answer: B | Question 2 Answer: B | Question 3 Answer: A | Question 4 Answer: C | Question 5 Answer: B |
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