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| Section | Objectives |
|---|---|
| Topic 1: Foundations of Algebra | - Equations and Inequalities
|
| Topic 2: Linear Functions and Systems | - Linear Equations
|
| Topic 3: Exponential and Logarithmic Concepts | - Exponential Functions
|
| Topic 4: Functions and Graphs | - Function Concepts
|
| Topic 5: Polynomial and Rational Expressions | - Polynomials
|
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NEW QUESTION # 93
The graph shows the number of customers, C(t), showing up to a store, where the number of hours since opening is along the horizontal axis and the number of customers showing up to the store each hour is along the vertical axis.
How can the concavity be described from t=6.2to t=10.1?
Answer: B
Explanation:
From t=6.2to about t=8.5, the graph is increasing, but it is becoming less steep as it approaches a local maximum.
That means the number of customers is:
" increasing slower and slower "
After the local maximum, from about t=8.5to t=10.1, the graph begins to decrease and becomes steeper downward.
That means the number of customers is:
" decreasing faster and faster "
So the full description is:
" The number of customers increases slower and slower and then decreases faster and faster. " Therefore, the correct answer is:
# ( " D " )
NEW QUESTION # 94
The scatterplot shows data on the number of shirts sold at a gift shop per week over time. The graphed regression function has an r
2
value of 0.09.
Which range of x-values is appropriate for extrapolation?
Answer: D
Explanation:
The r
2
value tells how closely the regression model fits the scatterplot data. In this problem, r
2
=0.09, which is extremely low. This means the regression model explains only a very small portion of the variation in the shirt-sales data. When r
2
is this weak, the model is not reliable for predictions outside the data range. Extrapolation is already less certain than interpolation because it predicts beyond the observed data. With such a poor fit, extending the model beyond the data would not be appropriate. Since 0.09 < 0.3, the best justification is that extrapolation is not appropriate because r
2
< 0.3. Therefore, the correct answer is C.
NEW QUESTION # 95
In the following graph showing the elevation profile, F(d), for a mountain biking course, the horizontal axis shows the number of miles since the start of the course and the vertical axis shows the elevation in feet.
How can the concavity be described from d=10 to d=13.1?
Answer: A
Explanation:
This question asks for a description of concavity and rate of change on a specific interval. From d=10 to part of the interval, the elevation is increasing, but the graph becomes less steep as it approaches a local maximum.
That means the elevation increases slower and slower. After the peak, the graph begins to decrease, and the downward slope becomes steeper. This means the elevation decreases faster and faster. The correct statement must describe both parts of the interval in order: first increasing at a slowing rate, then decreasing at an increasing rate. The other answer choices either reverse the behavior or describe the wrong direction of change. Therefore, the correct answer is A.
NEW QUESTION # 96
Through a local marketplace, a person makes livestock feeders to sell. The graph shows the functions modeling the cost and revenue.
What is the minimum number of livestock feeders that must be sold in order for the revenue to cover the costs?
Answer: C
Explanation:
This question asks for the break-even point, which is the point where:
Revenue=Cost
On the graph:
The solid blue line represents revenue.
The dashed blue line represents cost.
The revenue line starts below the cost line, meaning the person is not yet covering costs. The revenue line eventually crosses the cost line at a little more than 4 units.
Since the question asks for the minimum number of livestock feeders that must be sold, we need a whole number of feeders.
The graph shows the intersection occurs between:
4 and 5
So selling 4 feeders is not enough, but selling 5 feeders is enough for revenue to cover the costs.
Therefore, the correct answer is:
C
NEW QUESTION # 97
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 horizontal asymptote describes the long-term behavior of the function. In this problem, the graph shows a decreasing exponential model for the number of licensed sellers. The graph begins near a higher value and then decreases, eventually leveling off near 300. This means the number of licensed sellers approaches 300 over time. It does not mean the number necessarily becomes exactly 300 at 21 months, and it does not mean the sellers increase back to the initial value. The initial value is separate from the horizontal asymptote. Since the graph levels off around 300, the correct interpretation is that in the long run, the number of licensed sellers nears 300. Therefore, the answer is C.
NEW QUESTION # 98
......
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