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| Section | Objectives |
|---|---|
| Topic 1: Exponential Functions | - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions |
| Topic 2: Polynomial Functions | - Interpret concavity for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret rates of change for polynomial functions |
| Topic 3: Logistic Functions | - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions |
| Topic 4: Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on notation - Derive conclusions based on data |
| Topic 5: Validity of Models | - Determine validity - Determine fit - Examine utility |
| Topic 6: Graphical Depictions | - Interpret maximum and minimum for situations - Interpret concavity for situations - Interpret rates of change for situations - Interpret inputs and outputs for situations - Interpret asymptotes for situations |
| Topic 7: Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
>> Applied-Algebra Exam Topics <<
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NEW QUESTION # 31
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?
Answer: A
Explanation:
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 " )
NEW QUESTION # 32
The function P(t) represents the yearly profit, in thousands of dollars, for a virtual store since opening. The graph of P(t) is shown.
What is the time at which the store reached the maximum yearly profit?
Answer: C
Explanation:
The maximum value of a graph is the highest output value the function reaches. Since P(t) represents yearly profit, the maximum value occurs where the store earns its greatest yearly profit. The graph is a downward- opening curve, so its highest point is the vertex. To answer the question, we need the t-value of the vertex, not the profit amount. From the graph, the highest point occurs between 4 and 5 years after opening, closest to 4.5 years. This means the virtual store reached its maximum yearly profit approximately 4.5 years after it opened.
The later values decrease after the vertex, so options involving 7.5 or 14 years are not correct. Therefore, the correct answer is B.
NEW QUESTION # 33
The graph shows the number of people at an event venue after 3:00 p.m., in thousands.
Which rate of change is the greatest?
Answer: D
Explanation:
This graph represents a logistic growth function, which has an S-shaped curve:
Slow growth at the beginning (near point A)
Rapid growth in the middle (near point B and C)
Slowing growth at the end (near point D)
Key Concept:
Instantaneous rate of change = slope of the tangent line at a single point Average rate of change = slope between two points Analyze the graph:
At point A # slope is small (slow increase)
From A to C # increasing but not maximum
At point C # curve is steepest # maximum slope
From C to D # curve flattens # smaller slope
At point D # slope is very small (almost flat)
Conclusion:
The greatest rate of change occurs where the graph is steepest, which is at:
" Point C "
NEW QUESTION # 34
The figure displays the graphs of two functions representing the heights, h_1and h_2, in feet, of two balls tseconds after being launched.
Which ball was lower 0.9seconds after being launched?
Answer: A
Explanation:
This question asks us to compare the heights of two balls at a specific time:
t=0.9
The graph shows:
Ball 1 as the solid blue curve.
Ball 2 as the dashed blue curve.
To determine which ball was lower at t=0.9, we look at the vertical positions of both curves when the time is
0.9seconds.
At approximately t=0.9:
" height of Ball 1 " < " height of Ball 2 "
This means Ball 1 is lower than Ball 2 at that time.
The correct reasoning must say both:
Ball 1 was lower, and
Ball 1's height was less than Ball 2's height at t=0.9.
That matches option A.
NEW QUESTION # 35
A researcher collected data on the number of members in a national association over time. The results are shown in the scatterplot. The graphed regression function has an r
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