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| Section | Objectives |
|---|---|
| Topic 1: Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions |
| Topic 2: Validity of Models | - Examine utility - Determine fit - Determine validity |
| Topic 3: Logistic Functions | - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions - Interpret asymptotes for logistic functions |
| Topic 4: Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on notation - Derive conclusions based on graphs |
| Topic 5: Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Topic 6: Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Topic 7: Graphical Depictions | - Interpret concavity for situations - Interpret maximum and minimum for situations - Interpret rates of change for situations - Interpret inputs and outputs for situations - Interpret asymptotes for situations |
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NEW QUESTION # 45
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: D
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 # 46
The populations, in thousands, of two towns are shown in the graph, where the horizontal axis measures the time in years.
Which town's population is growing at a faster rate?
Answer: D
Explanation:
To decide which town is growing faster, compare the slopes of the two lines. In a linear population graph, the slope represents the growth rate, while the starting value represents the initial population. The graph shows that Town A has a slope of about 1.0 thousand people per year, while Town B has a slope of about 0.7 thousand people per year. Since 1.0 > 0.7, Town A is growing at a faster rate. The values 6.5 and 5.5 refer to population amounts, not growth rates, so they do not answer the question. The correct comparison must use the slopes. Therefore, the correct answer is D.
NEW QUESTION # 47
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: C
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 # 48
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: D
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 # 49
The number of property sales in a region this year is expected to be 9 more than 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 140?
Answer: C
Explanation:
This question asks for correct function notation. The input x represents the number of properties sold last year, and the output H(x) represents the expected number of property sales this year. Since this year's number is expected to be 9 more than last year's number, the function rule is H(x)=x+9. The problem states that 140 properties were sold last year, so the correct input is x=140. Substituting gives H(140)=140+9=149. This means that when last year's sales were 140, this year's expected sales are 149. The input must be inside the parentheses, and the output must follow the equals sign. Therefore, the correct answer is B.
NEW QUESTION # 50
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