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| Section | Objectives |
|---|---|
| Topic 1: Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions |
| Topic 2: Graphical Depictions | - Interpret inputs and outputs for situations - Interpret concavity for situations - Interpret rates of change for situations - Interpret maximum and minimum for situations - Interpret asymptotes for situations |
| Topic 3: Exponential Functions | - Interpret rates of change for exponential functions - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions |
| Topic 4: Validity of Models | - Examine utility - Determine validity - Determine fit |
| Topic 5: Logistic Functions | - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions |
| Topic 6: Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Topic 7: Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on data - Derive conclusions based on notation |
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質問 # 58
The number of employees under supervisor B is 13 more than the number of employees under supervisor A.
Let F(n)represent the number of employees under the two supervisors, where nis the number of employees under supervisor A and Fis the number of employees under supervisor B.
Which is the correct function to represent this relationship?
正解：D
解説：
We are told that supervisor B has 13 more employees than supervisor A.
Let:
n= " number of employees under supervisor A "
and
F(n)= " number of employees under supervisor B "
The phrase "13 more than" means we add 13:
F(n)=n+13
So, if supervisor A has nemployees, supervisor B has 13 additional employees.
For example, if supervisor A had 20 employees, then supervisor B would have:
F(20)=20+13=33
Therefore, the correct answer is:
# ( " C " )
質問 # 59
A team was assembled at a manufacturing plant in order to boost productivity. The team was tasked with producing as many widgets each day as possible. The results are shown in the graph.
What is the correct interpretation of the average rate of change from day 6 to day 14?
正解：B
解説：
The graph models the number of widgets the team can produce each day.
The horizontal axis represents:
" days "
The vertical axis represents:
" widgets "
The graph gives two labeled points:
(6#3.4)
and
(14#23)
The average rate of change is:
" change in widgets " / " change in days "
Substitute the values:
(23-3.4)/(14-6)
=19.6/8
=2.45
Rounded to the nearest tenth:
2.5
This means the team increased production by an average of approximately:
2.5 " widgets each day "
Therefore, the correct answer is:
# ( " B " )
質問 # 60
The number of wild horses in a federal park is represented by the logistic function f(x), whose graph is shown, where xrepresents the number of years since the park was established and f(x)represents the wild horse population in a given year.
How does the number of wild horses change as time progresses from year 1 to year 9?
正解：D
解説：
The graph is a logistic growth function.
A logistic function often has an S-shape. It begins by increasing slowly, then increases faster and faster, and later levels off as it approaches a maximum carrying capacity.
From year 1 to year 9, the graph is rising and becoming steeper.
That means:
" the wild horse population is increasing "
and the slope is getting larger, so:
" the population is increasing faster and faster "
Therefore, the correct answer is:
# ( " A " )
質問 # 61
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?
正解：D
解説：
We are told that computer B completes 12 more tasks than computer A.
Let:
x= " number of tasks completed by computer A "
and
F(x)= " number of tasks completed by computer B "
The phrase "12 more than" means add 12 to the original amount:
F(x)=x+12
So, if computer A completes xtasks, computer B completes:
x+12
tasks.
For example, if computer A completed 50 tasks, then computer B completed:
F(50)=50+12=62
Therefore, the correct answer is:
# ( " B " )
質問 # 62
A new company just launched and is using the function M(t) to predict its market share after t years. The graph of M(t) is shown.
When should the company expect to have a market share of 60%?
正解：B
解説：
This question uses a logistic function, which often models growth that starts slowly, increases rapidly, and then levels off near a maximum value. The input t represents years, and M(t) represents market share as a percent. To find when the company reaches a 60% market share, locate 60 on the vertical axis and identify where the graph reaches that height. Then read the corresponding value on the horizontal axis. From the graph, the curve reaches 60% slightly after 6 years, approximately at t=6.6. The value after 6 years is close but not yet at 60%. Therefore, the company should expect to reach 60% market share after about 6.6 years.
The correct answer is D.
質問 # 63
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