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| Section | Objectives |
|---|---|
| Topic 1: Graphical Depictions | - Interpret inputs and outputs for situations - Interpret rates of change for situations - Interpret concavity for situations - Interpret maximum and minimum for situations - Interpret asymptotes for situations |
| Topic 2: Logistic Functions | - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions |
| Topic 3: Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions |
| Topic 4: Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on data - Derive conclusions based on notation |
| Topic 5: Validity of Models | - Determine fit - Examine utility - Determine validity |
| Topic 6: Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Topic 7: Exponential Functions | - Interpret rates of change for exponential functions - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions |
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問題 #100
The function f(z) represents the relationship between the number of units in two inventories, where z is the number of units in inventory A and f(z) is the number of units in inventory B. The number of units in inventory B is 2 more than the number of units in inventory A. Which function represents this situation?
答案：D
解題說明：
This problem translates a verbal statement into function notation. The variable z represents the number of units in inventory A, and f(z) represents the number of units in inventory B. The phrase "2 more than" tells us to add 2 to the number of units in inventory A. That gives the rule f(z)=z+2. For example, if inventory A has
10 units, then inventory B has f(10)=12 units. Option A subtracts 2, option C multiplies by 2, and option D divides by 2, so those do not match the stated relationship. Because inventory B is always exactly 2 more than inventory A, the correct function is f(z)=z+2. Therefore, the answer is B.
問題 #101
A new company just launched and is using the function M(t)to predict its market share after tyears. The graph of M(t)is shown.
When should the company expect to have a market share of 60%?
答案：A
解題說明：
The function M(t)represents the company's predicted market share after tyears.
The horizontal axis represents:
t= " time in years "
The vertical axis represents:
M(t)= " market share percentage "
We need to find when the company's market share reaches:
60%
To answer this from the graph:
Locate 60on the vertical axis.
Move horizontally until reaching the blue curve.
Move downward to the horizontal axis to read the corresponding time.
From the graph, the blue curve reaches 60%a little after 6years, approximately at:
t=6.6
So the company should expect to have a market share of 60%after about:
6.6 " years "
問題 #102
A new company just launched and is using the function M(t)to predict its market share after tyears. The graph of M(t)is shown.
When should the company expect to have a market share of 40%?
答案：A
解題說明：
The function M(t)represents the company's market share after tyears.
The horizontal axis represents:
t= " time in years "
The vertical axis represents:
M(t)= " market share percentage "
We need to find when the market share reaches:
40%
From the graph, locate 40on the vertical axis. Then move horizontally to the blue curve and read the corresponding value on the horizontal axis.
The curve reaches 40%at approximately:
t=7.4
So the company should expect to have a market share of 40%after about:
7.4 " years "
Therefore, the correct answer is:
# ( " C " )
問題 #103
The graph shows the number of books, N, checked out from a library each week. The number of weeks since the beginning of the year is on the horizontal axis, and the number of books checked out per week is on the vertical axis. Point A represents 165 books checked out in the first week, or N(0)=165. Which statement represents an accurate conclusion?
Exhibit:
答案：D
解題說明：
This question asks for the correct interpretation of a labeled point on a graph. In function notation, N(x)=y means when the input is x weeks, the output is y books checked out. The exhibit shows several plotted points.
Point B is located at approximately x=2.8 and y=177, so Point B represents N(2.8)=177. To verify a graph statement, both the horizontal coordinate and vertical coordinate must match the actual point on the graph. If either coordinate is wrong, then the statement is not accurate. Since Point B matches the stated coordinates and output value, it is the valid conclusion. Therefore, the correct answer is A.
問題 #104
Through a local marketplace, a person makes livestock feeders to sell. The graph shows the functions modeling the cost and revenue.
What is the minimum number of livestock feeders that must be sold in order for the revenue to cover the costs?
答案：D
解題說明：
This question asks for the break-even point, which is the point where:
Revenue=Cost
On the graph:
The solid blue line represents revenue.
The dashed blue line represents cost.
The revenue line starts below the cost line, meaning the person is not yet covering costs. The revenue line eventually crosses the cost line at a little more than 4 units.
Since the question asks for the minimum number of livestock feeders that must be sold, we need a whole number of feeders.
The graph shows the intersection occurs between:
4 and 5
So selling 4 feeders is not enough, but selling 5 feeders is enough for revenue to cover the costs.
Therefore, the correct answer is:
C
問題 #105
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