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| Section | Objectives |
|---|---|
| Topic 1: Graphical Depictions | - Interpret asymptotes for situations - Interpret rates of change for situations - Interpret maximum and minimum for situations - Interpret inputs and outputs for situations - Interpret concavity for situations |
| Topic 2: Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on data - Derive conclusions based on graphs |
| Topic 3: Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions |
| Topic 4: Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Topic 5: Logistic Functions | - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions |
| Topic 6: Validity of Models | - Determine validity - Determine fit - Examine utility |
| Topic 7: Exponential Functions | - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions |
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69. Frage
As regulations change, the number of licensed sellers of a product decreases. The graph models the change in the number of licensed sellers over time.
What does the horizontal asymptote mean?
Antwort: A
Begründung:
The graph shows a decreasing exponential model.
The vertical axis represents:
" Licensed sellers "
The horizontal axis represents:
" Time in years "
The graph starts near 700 licensed sellers and decreases over time. However, it does not appear to decrease all the way to 0. Instead, it levels off near:
y=100
That horizontal line is the horizontal asymptote.
A horizontal asymptote represents the long-term value the function approaches as time continues.
So the correct interpretation is:
" In the long run, the number of licensed sellers nears 100. "
Therefore, the correct answer is:
# ( " C " )
70. Frage
A team was assembled at a manufacturing plant in order to boost productivity. The team was tasked with producing as many widgets each day as possible. The results are shown in the graph.
What is the correct interpretation of the average rate of change from day 6 to day 14?
Antwort: B
Begründung:
The graph models the number of widgets the team can produce each day.
The horizontal axis represents:
" days "
The vertical axis represents:
" widgets "
The graph gives two labeled points:
(6#3.4)
and
(14#23)
The average rate of change is:
" change in widgets " / " change in days "
Substitute the values:
(23-3.4)/(14-6)
=19.6/8
=2.45
Rounded to the nearest tenth:
2.5
This means the team increased production by an average of approximately:
2.5 " widgets each day "
Therefore, the correct answer is:
# ( " B " )
71. Frage
The temperature of an object changes according to the relationship in the graph.
Which equation represents the horizontal asymptote of the function?
Antwort: B
Begründung:
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