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| Section | Objectives |
|---|---|
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Validity of Models | - Determine validity - Examine utility - Determine fit |
| Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions |
| Logistic Functions | - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions |
| Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on graphs - Derive conclusions based on notation |
| Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions - Interpret rates of change for exponential functions |
| Graphical Depictions | - Interpret rates of change for situations - Interpret inputs and outputs for situations - Interpret maximum and minimum for situations - Interpret asymptotes for situations - Interpret concavity for situations |
>> Applied-Algebraテストトレーニング <<
Applied-Algebra学習教材の練習試験や模擬試験はみんなにとって重要です。今のリビジョン条件はApplied-Algebra試験に参加する良い機会です。したがって、レビュープランを調整するために、Applied-Algebraの各練習問題を要約することが不可欠です。今、私たちはApplied-Algebra実際試験を模擬するためにオンラインテストエンジンとWindowsソフトウェアを追加しました。
質問 # 130
The number of property sales in a region this year is expected to be 3 times the number of property sales in the region last year. The function H(x) represents the number of property sales this year, where x represents the number of properties sold last year. Which notation represents the number of property sales this year, given that the number of properties sold last year was 280?
正解：C
解説：
This problem uses function notation to describe a multiplicative relationship. The input x is the number of properties sold last year, and the output H(x) is the expected number sold this year. Since this year's sales are
3 times last year's sales, the function rule is H(x)=3x. The given input is 280 because 280 properties were sold last year. Substituting gives H(280)=3(280)=840. That means 840 property sales are expected this year. The answer choice must show the correct input of 280 and the correct output of 840. The other options either reverse the values or use an incorrect output. Therefore, the correct answer is C.
質問 # 131
The number of property sales in a region this year is expected to be 6 less than the number of property sales in the region last year. The function H(x)represents the number of property sales this year, where xrepresents the number of properties sold last year.
Which notation represents the number of property sales this year, given that the number of properties sold last year was 330?
正解：A
解説：
We are told that this year's number of property sales is 6 less than last year's number of property sales.
Let:
x= " number of properties sold last year "
and
H(x)= " number of property sales this year "
Since this year's sales are 6 less than last year's sales, the function rule is:
H(x)=x-6
The question says that the number of properties sold last year was:
x=330
Substitute 330into the function:
H(330)=330-6
H(330)=324
So the notation that correctly represents the number of property sales this year is:
H(330)=324
This means: if 330 properties were sold last year, then 324 properties are expected to be sold this year.
質問 # 132
The data in the scatterplot represents the number of monthly train crossings at a particular intersection over time.
Which type of function should be used to model the data?
正解：B
解説：
The scatterplot shows the number of monthly train crossings decreasing over time. The decrease is not constant from one year to the next, so a linear model is not the best choice. Instead, the data decreases quickly at first and then begins to level off, which is characteristic of exponential decay. Exponential models are appropriate when a quantity changes by a repeated factor or percentage over equal time intervals. A logistic model would usually show an S-shaped pattern with a carrying capacity, and a polynomial model would be more appropriate for turning points or more complex curvature. Since the points show a smooth decreasing curve that flattens over time, an exponential function best models the data. Therefore, the correct answer is B.
質問 # 133
The function f(n) represents the relationship between the distances traveled by two vehicles, where n is the distance traveled by vehicle A and f is the distance traveled by vehicle B. The distance traveled by vehicle B is 17 more than the distance traveled by vehicle A.
Which function represents this situation?
正解：B
解説：
The function f(n) gives the distance traveled by vehicle B.
The input n represents the distance traveled by vehicle A.
The problem says vehicle B travels 17 more than vehicle A. The phrase "17 more than" means we add 17 to the amount traveled by vehicle A.
So the relationship is:
f(n)=n+17
For example, if vehicle A traveled 50 miles, then vehicle B traveled:
f(50)=50+17=67
So the correct function is:
f(n)=n+17
Therefore, the correct answer is:
B
質問 # 134
The temperature of an object changes according to the relationship in the graph.
Which equation represents the horizontal asymptote of the function?
正解：B
解説：
The graph shows the temperature of an object changing over time.
The horizontal axis represents:
" Time in minutes "
The vertical axis represents:
" Temperature in degrees Fahrenheit "
The curve is decreasing quickly at first and then begins to level off. This is the shape of an exponential decay function.
A horizontal asymptote is a horizontal line that the graph approaches as time increases.
Because a horizontal asymptote is a horizontal line, its equation must have the form:
y= " constant "
From the graph, the temperature approaches about:
25