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| Section | Objectives |
|---|---|
| Logistic Functions | - Interpret asymptotes for logistic functions - Interpret rates of change for logistic functions - Interpret inputs and outputs for logistic functions |
| Functions and Algebra of Functions | - Derive conclusions based on notation - Derive conclusions based on data - Derive conclusions based on graphs |
| Exponential Functions | - Interpret concavity for exponential functions - Interpret inputs and outputs for exponential functions - Interpret rates of change for exponential functions |
| Validity of Models | - Determine validity - Examine utility - Determine fit |
| Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions |
| Graphical Depictions | - Interpret concavity for situations - Interpret asymptotes for situations - Interpret maximum and minimum for situations - Interpret rates of change for situations - Interpret inputs and outputs for situations |
| Linear Functions | - Interpret inputs and outputs of linear functions - Interpret rates of change for linear functions |
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NEW QUESTION # 132
The number of members of a religious organization can be modeled using the logistic function f(x), where xrepresents the number of years since the organization was started and f(x)represents the number of members.
The graph of f(x)is shown.
What is one range of values for which the graph is concave down?
Answer: D
Explanation:
The graph is a logistic growth curve.
A logistic growth curve has two main concavity regions:
" concave up before the inflection point "
and
" concave down after the inflection point "
From the graph, the function increases faster and faster until about:
x=6
After x=6, the graph continues increasing, but it begins to flatten out. That means the number of members is increasing slower and slower.
This is concave down behavior.
Therefore, one interval where the graph is concave down is:
(6#11)
So the correct answer is:
# ( " D " )
NEW QUESTION # 133
The number of property sales in a region this year is expected to be 6 less than the number of property sales in the region last year. The function H(x)represents the number of property sales this year, where xrepresents the number of properties sold last year.
Which notation represents the number of property sales this year, given that the number of properties sold last year was 330?
Answer: A
Explanation:
We are told that this year's number of property sales is 6 less than last year's number of property sales.
Let:
x= " number of properties sold last year "
and
H(x)= " number of property sales this year "
Since this year's sales are 6 less than last year's sales, the function rule is:
H(x)=x-6
The question says that the number of properties sold last year was:
x=330
Substitute 330into the function:
H(330)=330-6
H(330)=324
So the notation that correctly represents the number of property sales this year is:
H(330)=324
This means: if 330 properties were sold last year, then 324 properties are expected to be sold this year.
NEW QUESTION # 134
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: C
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 # 135
Consider the graph of h(t) shown. The function represents the height, h, in feet, of a ball t seconds after being launched.
What is the point, if any, at which the concavity changes from concave down to concave up?
Answer: A
Explanation:
The graph represents the height of a launched ball over time. Such height functions are typically quadratic because gravity causes the ball to rise, slow down, reach a maximum height, and then fall. The graph shown is a downward-opening parabola. A downward-opening parabola is concave down for its entire domain.
Concavity changes only if the curve switches from bending downward to bending upward, or from bending upward to bending downward. Since this graph bends downward the entire time, there is no point where the concavity changes from concave down to concave up. The vertex is a maximum point, but it is not a change in concavity. Therefore, the correct statement is that the graph is always concave down.
NEW QUESTION # 136
The populations, in thousands, of two towns are shown in the graph, where the horizontal axis measures the time in years.
Which town's population is growing at a faster rate?
Answer: D
Explanation:
To determine which town's population is growing faster, compare the slopes of the two lines. In a linear population model, the slope represents the growth rate, while the starting value represents the initial population. The graph shows that Town A and Town B both increase over time, but Town B has the larger slope. Town B grows at about 1.3 thousand people per year, while Town A grows at about 1.1 thousand people per year. Since 1.3 > 1.1, Town B's population is increasing at a faster rate. The values 6.5 and 5.5 describe starting population amounts, not growth rates. Therefore, the correct answer is A.
NEW QUESTION # 137
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