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| Section | Objectives |
|---|---|
| Topic 1: Validity of Models | - Examine utility - Determine fit - Determine validity |
| Topic 2: Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on graphs - Derive conclusions based on data |
| 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: Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions |
| Topic 5: Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Topic 6: Logistic Functions | - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions |
| Topic 7: Graphical Depictions | - Interpret concavity for situations - Interpret asymptotes for situations - Interpret inputs and outputs for situations - Interpret maximum and minimum for situations - Interpret rates of change for situations |
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NEW QUESTION # 73
The number of people auditioning for a game show is expected to be 3 less than the number of people who auditioned last year. The function A(t)can be used to model the situation, where trepresents the number of people who auditioned last year and Arepresents the number of people expected to audition this year.
Which quantity represents the number of people expected to audition this year, given that 280 people auditioned last year?
Answer: A
Explanation:
The function A(t)represents the number of people expected to audition this year.
The input trepresents the number of people who auditioned last year.
The problem says this year's number is expected to be 3 less than last year's number. Therefore, the function rule is:
A(t)=t-3
We are told that 280 people auditioned last year, so:
t=280
Substitute 280into the function:
A(280)=280-3
A(280)=277
So, the notation that represents the number of people expected to audition this year is:
A(280)=277
This means if 280 people auditioned last year, then 277 people are expected to audition this year.
Therefore, the correct answer is:
# ( " A " )
NEW QUESTION # 74
The population of fish in a lake is changing according to the function
P(t)=462-35t
where tis the number of months since the beginning of the year and P(t)is the fish population at time t.
Which interpretation of the rate of change is correct?
Answer: B
Explanation:
The function is:
P(t)=462-35t
This is a linear function in the form:
P(t)=mt+b
where:
m= " rate of change "
and
b= " initial value "
In this function:
m=-35
The negative sign means the fish population is decreasing.
The number 35tells us the amount of decrease per month.
So the fish population is decreasing by:
35 " fish per month "
The value 462is not the rate of change. It represents the starting fish population at the beginning of the year, when t=0:
P(0)=462
Therefore, the correct interpretation is:
" The number of fish in the lake is decreasing at a constant rate of 35 fish per month. " So the correct answer is:
# ( " D " )
NEW QUESTION # 75
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: D
NEW QUESTION # 76
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:
Answer: B
Explanation:
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.
NEW QUESTION # 77
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?
Answer: B
Explanation:
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 " )
NEW QUESTION # 78
......
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