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| Section | Objectives |
|---|---|
| Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on graphs - Derive conclusions based on data |
| Logistic Functions | - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions |
| Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Validity of Models | - Determine validity - Examine utility - Determine fit |
| Exponential Functions | - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions |
| Graphical Depictions | - Interpret inputs and outputs for situations - Interpret asymptotes for situations - Interpret rates of change for situations - Interpret maximum and minimum for situations - Interpret concavity for situations |
| Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions |
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NEW QUESTION # 46
The number of people auditioning for a game show is expected to be 7 more than the number of people who auditioned last year. The function A(t) can be used to model the situation, where t represents the number of people who auditioned last year and A(t) represents the number of people expected to audition this year.
Which quantity represents the number of people expected to audition this year, given that 440 people auditioned last year?
Answer: D
Explanation:
In this function-notation problem, the input represents last year's number of people and the output represents this year's expected number. Because this year's number is 7 more than last year's, the rule is A(t)=t+7. The question says 440 people auditioned last year, so the correct input is 440. Substituting gives A(440)
=440+7=447. This means if 440 people auditioned last year, then 447 are expected to audition this year. The notation must place 440 inside the parentheses because that is the input value, and 447 must be written as the output value. The other options reverse the input and output or subtract instead of adding. Therefore, option C is correct.
NEW QUESTION # 47
A person makes down quilts to sell.
The graph shows the functions that model the cost and revenue.
How many down quilts need to sell to break even/start making a profit?
Answer: C
Explanation:
This question asks us to interpret a graph showing cost and revenue.
In Applied Algebra, the break-even point is where:
" Revenue " = " Cost "
On a graph, this happens where the revenue line and the cost line intersect.
From the graph:
The solid blue line represents revenue.
The dashed blue line represents cost.
The break-even point occurs where these two lines cross.
Looking carefully at the graph, the two lines intersect at approximately:
x=6
The horizontal axis represents the number of units, meaning the number of down quilts sold.
So the person needs to sell about:
6 " quilts "
to break even.
After selling more than 6 quilts, the revenue line is above the cost line, meaning the person begins making a profit.
NEW QUESTION # 48
The graph shows the number of people waiting in a virtual queue to buy tickets for an event.
What does the horizontal asymptote mean?
Answer: C
Explanation:
The graph shows the queue size changing over time.
The horizontal axis represents:
" Time in minutes "
The vertical axis represents:
" Queue size "
The graph is a decreasing exponential curve. It starts near 750people and decreases quickly at first. Then the curve begins to flatten near:
y=100
A horizontal asymptote is the horizontal line that the graph approaches as time continues.
Here, the graph approaches the horizontal line:
y=100
This means that as time passes, the number of people in the virtual queue gets closer and closer to 100.
It does not mean the queue decreases to 0, because the graph levels off near 100, not near 0.
Therefore, the correct interpretation is:
" As time passes, the number of people in the queue approaches 100. "
NEW QUESTION # 49
A coach is placing an order for team shirts. The graph shows the total cost based on the number of shirts.
What is the cost of each additional shirt?
Exhibit:
Answer: A
Explanation:
This question asks for the cost of each additional shirt, which is the slope of the linear graph. The slope tells how much the total cost increases for each increase of 1 shirt. From the exhibit, the graph shows a starting cost near $39 and a point near (10, 139). The increase in cost from 0 shirts to 10 shirts is 139#39=100 dollars.
Dividing by 10 shirts gives a rate of 10 dollars per shirt. The fixed starting cost is not the cost of a shirt; it is the initial fee or setup cost. Since the graph rises by $10 for each additional shirt, the cost per additional shirt is $10.00. Therefore, the answer is B.
NEW QUESTION # 50
The function P(t)represents the weekly profit, in thousands of dollars, for a rental store since opening. The graph of P(t)is shown.
When did the store have its maximum weekly profit?
Answer: B
Explanation:
The graph shows:
P(t)= " weekly profit in thousands of dollars "
where:
t= " years since opening "
The graph is a downward-opening curve, so it has a maximum value at its highest point. In Applied Algebra, the highest point of this kind of polynomial graph is called the vertex.
To answer the question, we need the t-value of the vertex because the question asks when the store had its maximum weekly profit.
From the graph, the highest point occurs between:
t=5
and
t=6
More specifically, it is approximately:
t=5.5
So the store had its maximum weekly profit approximately:
5.5 " years after opening "
NEW QUESTION # 51
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