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| Section | Objectives |
|---|---|
| Topic 1: Exponential and Logarithmic Concepts | - Exponential Functions
|
| Topic 2: Foundations of Algebra | - Equations and Inequalities
|
| Topic 3: Functions and Graphs | - Graphing Functions
|
| Topic 4: Linear Functions and Systems | - Linear Equations
|
| Topic 5: Polynomial and Rational Expressions | - Polynomials
|
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NEW QUESTION # 131
In the graph showing the number of new customer accounts, the horizontal axis shows the number of weeks since the beginning of winter and the vertical axis shows the number of new customer accounts. More customer accounts are opened during snowy weeks than during weeks without snow.
When was it likely snowy?
Answer: A
Explanation:
This question asks us to interpret unusually high values on a graph. The problem states that more customer accounts are opened during snowy weeks than during weeks without snow. Therefore, the likely snowy weeks correspond to the peaks on the graph, where the number of new customer accounts is noticeably higher than surrounding weeks. The graph shows clear spikes at approximately week 7 and week 14. These weeks have higher account openings compared with nearby weeks, making them the best evidence of snowy conditions.
Week 1 and week 5 do not match the main peaks shown in the graph. Since the snowy weeks should correspond to the highest customer-account values, the correct answer is D.
NEW QUESTION # 132
A recipe calls for a constant ratio of water and lemon juice. The graph shows the relationship between the amounts of these two ingredients, where wis the volume of water and lis the volume of lemon juice.
What is the correct interpretation of the rate of change?
Answer: A
Explanation:
The graph shows a linear relationship between:
w= " water in cups "
and
l= " lemon juice in cups "
The line passes through the origin, so the relationship has the form:
l=mw
where mis the rate of change.
From the graph, a clear point on the line is approximately:
(8#5)
This means when there are 8 cups of water, there are 5 cups of lemon juice.
The rate of change is:
m= " change in lemon juice " / " change in water "
m=5/8
So the relationship is:
l=5/8 w
This means the amount of lemon juice must be:
5/8
of the amount of water.
NEW QUESTION # 133
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: A
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 # 134
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: B
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 # 135
The logistic function f(x), whose graph is shown, models the number of people who have created a website account, where xrepresents the number of days since the website started and f(x)represents the number of people who have created an account.
What is one range of values for which the graph is concave down?
Answer: A
Explanation:
For a logistic graph, concavity changes at the inflection point.
Before the inflection point, the graph is usually concave up. This means the function is increasing faster and faster.
After the inflection point, the graph is concave down. This means the function is still increasing, but it is increasing slower and slower.
From the graph, the curve changes concavity around:
x=8
After x=8, the graph begins to level off as it approaches its upper limit.
So one interval where the graph is concave down is:
(8#16)
Therefore, the correct answer is:
# ( " A " )
NEW QUESTION # 136
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