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| Section | Objectives |
|---|---|
| Topic 1: Functions and Algebra of Functions | - Derive conclusions based on graphs - Derive conclusions based on notation - Derive conclusions based on data |
| Topic 2: Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
| Topic 3: Graphical Depictions | - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret concavity for situations - Interpret inputs and outputs for situations - Interpret rates of change for situations |
| Topic 4: Exponential Functions | - Interpret concavity for exponential functions - Interpret rates of change for exponential functions - Interpret inputs and outputs for exponential functions |
| Topic 5: Logistic Functions | - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions - Interpret asymptotes for logistic functions |
| Topic 6: Polynomial Functions | - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions - Interpret rates of change for polynomial functions |
| Topic 7: Validity of Models | - Determine fit - Examine utility - Determine validity |
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NEW QUESTION # 78
A researcher collected data on the number of annual bear sightings in a region over time. The results are shown in the scatterplot. The graphed regression function has an r
2value of 0.41. The predicted number of annual bear sightings after 19.4 years is 88.5.
Is this prediction appropriate?
Answer: C
Explanation:
The r2value of 0.41 indicates a moderate fit, not a strong fit. A moderate regression model may sometimes support limited extrapolation, but only if the prediction stays close to the observed data. Here, the prediction is made at x=19.4, which is beyond the maximum x-value shown in the scatterplot. For a moderate fit, extrapolation should be more conservative than for a strong fit. The value x=19.4 is more than 25% of the data range beyond the maximum observed value, so the prediction is too far outside the data. Because the fit is only moderate and the extrapolation distance is too large, the prediction is not appropriate. Therefore, the answer is B.
NEW QUESTION # 79
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: B
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 # 80
As sacks are unloaded off a wagon, the total weight of the wagon and sacks changes. Each sack has the same weight. After 3 sacks are removed, the total weight of the cart and remaining sacks is 116 pounds. After 6 sacks are removed, the total weight is 101 pounds.
What is the weight of each sack?
Answer: B
Explanation:
This situation can be modeled using a linear relationship because each sack has the same weight.
We are given:
After 3sacks are removed, the total weight is 116pounds.
After 6sacks are removed, the total weight is 101pounds.
From 3 sacks removed to 6 sacks removed, the number of removed sacks increases by:
6-3=3
During that time, the total weight decreases from 116pounds to 101pounds:
116-101=15
So removing 3 additional sacks decreases the total weight by 15 pounds.
Now divide to find the weight of one sack:
15/3=5
So each sack weighs:
5 " pounds "
Check:
If 3 more sacks are removed and each sack weighs 5 pounds, the total weight should decrease by:
3(5)=15
116-15=101
This matches the given information.
NEW QUESTION # 81
The traffic flow on a roadway after 8:00 a.m. is modeled by the graphed exponential function.
Which conclusion is valid, based on the horizontal asymptote?
Answer: D
Explanation:
The graph shows an exponential decay model for traffic flow. A horizontal asymptote represents the long- term value the function approaches. In this case, the graph decreases but levels off above zero. Because the horizontal asymptote is above the horizontal axis, the model predicts that the traffic flow approaches a positive number rather than decreasing all the way to zero. Exponential functions do not change by a constant additive rate; that is a property of linear functions. Instead, exponential models change by a constant factor.
Therefore, statements about constant rate are not valid here. The valid conclusion based on the asymptote is that the traffic flow will not decrease to 0 vehicles per hour. The correct answer is B.
NEW QUESTION # 82
Based on collected data, the number of registered voters in a district can be modeled using the function f(x)=1,300× # 0.92 #
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