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| Section | Objectives |
|---|---|
| Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions |
| Logistic Functions | - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions |
| Graphical Depictions | - Interpret asymptotes for situations - Interpret rates of change for situations - Interpret inputs and outputs for situations - Interpret concavity for situations - Interpret maximum and minimum for situations |
| Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on notation - Derive conclusions based on graphs |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Validity of Models | - Examine utility - Determine validity - Determine fit |
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NEW QUESTION # 90
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?
Answer: A
Explanation:
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.
NEW QUESTION # 91
The number of letters processed daily at a mail center is modeled by the decreasing exponential function shown in the graph.
What is the long-term trend in the number of letters processed per day, based on the equation of the horizontal asymptote?
Answer: A
Explanation:
In an exponential decay model, the horizontal asymptote represents the long-term value that the function approaches as time increases. The graph shows the number of letters processed per day decreasing quickly at first and then leveling off. Since the graph approaches the horizontal line y=1000, the long-term trend is 1,000 letters per day. This does not mean the mail center immediately processes exactly 1,000 letters, but it means the model predicts the daily number will get closer and closer to 1,000 over time. The other choices either represent values too low or values from earlier parts of the graph, not the asymptote. Therefore, the correct answer is B.
NEW QUESTION # 92
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?
Answer: B
Explanation:
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
NEW QUESTION # 93
The value of an investment portfolio after x years is modeled by the function g(x)=3100(1.059) x
.
What is the value of the portfolio when x=10?
Answer: B
Explanation:
This problem uses an exponential growth model. The initial portfolio value is 3100, and the growth factor is
1.059. Since the growth factor is greater than 1, the portfolio increases over time. To find the value after 10 years, substitute x=10 into the function: g(10)=3100(1.059)
10
First evaluate the exponent, then multiply by 3100. This gives g(10)#5499.4758. Rounded to the nearest cent, the value is $5,499.48. The answer must be written as money because the function models the value of an investment portfolio. Among the choices, only option B matches the correctly evaluated exponential expression. Therefore, the correct answer is B.
NEW QUESTION # 94
The number of members of a religious organization can be modeled using the logistic function f(x), where xrepresents the number of years since the organization was started and f(x)represents the number of members.
The graph of f(x)is shown.
What is one range of values for which the graph is concave down?
Answer: C
Explanation:
The graph is a logistic growth curve.
A logistic growth curve has two main concavity regions:
" concave up before the inflection point "
and
" concave down after the inflection point "
From the graph, the function increases faster and faster until about:
x=6
After x=6, the graph continues increasing, but it begins to flatten out. That means the number of members is increasing slower and slower.
This is concave down behavior.
Therefore, one interval where the graph is concave down is:
(6#11)
So the correct answer is:
# ( " D " )
NEW QUESTION # 95
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