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| Section | Objectives |
|---|---|
| Topic 1: Linear Functions | - Interpret rates of change for linear functions - Interpret inputs and outputs of linear functions |
| Topic 2: Exponential Functions | - Interpret inputs and outputs for exponential functions - Interpret concavity for exponential functions - Interpret rates of change for exponential functions |
| Topic 3: Polynomial Functions | - Interpret rates of change for polynomial functions - Interpret inputs and outputs for polynomial functions - Interpret concavity for polynomial functions |
| Topic 4: Functions and Algebra of Functions | - Derive conclusions based on data - Derive conclusions based on notation - Derive conclusions based on graphs |
| Topic 5: Validity of Models | - Determine validity - Determine fit - Examine utility |
| Topic 6: Logistic Functions | - Interpret asymptotes for logistic functions - Interpret inputs and outputs for logistic functions - Interpret rates of change for logistic functions |
| Topic 7: Graphical Depictions | - Interpret rates of change for situations - Interpret maximum and minimum for situations - Interpret asymptotes for situations - Interpret inputs and outputs for situations - Interpret concavity for situations |
>> Frenquent Applied-Algebra Update <<
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NEW QUESTION # 12
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 # 13
As sacks are unloaded off a wagon, the total weight of the wagon and sacks changes. Each sack has the same weight. After 5 sacks are removed, the total weight of the wagon and remaining sacks is 135 pounds. After 9 sacks are removed, the total weight is 87 pounds. What is the weight of each sack?
Answer: D
Explanation:
This situation has a constant rate of change because each sack weighs the same amount. After 5 sacks are removed, the total weight is 135 pounds. After 9 sacks are removed, the total weight is 87 pounds. From 5 to
9 sacks removed is 4 more sacks. Over the same interval, the total weight decreases by 135#87=48 pounds.
Since 4 sacks account for a 48-pound decrease, each sack must weigh 48รท4=12 pounds. This uses the linear idea that equal changes in the input produce equal changes in the output. Therefore, the weight of each sack is
12 pounds, which is answer A.
NEW QUESTION # 14
The function N(t)models the number of subscribers to a virtual newsletter over time. The graph of N(t)is shown. The horizontal axis represents the number of years since the newsletter started, and the vertical axis represents the number of subscribers, in thousands.
How is the number of subscribers changing over time based on the graph?
Answer: A
Explanation:
The graph shows an increasing exponential curve.
The number of subscribers is going up as time passes, so the function is increasing.
Also, the graph becomes steeper as time increases. This means the rate of increase is getting larger.
So the number of subscribers is:
" increasing faster and faster "
This is a key feature of exponential growth.
NEW QUESTION # 15
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: D
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 # 16
A researcher collected data on the traffic frequency on a section of road. The results are shown in the scatterplot. A regression function is graphed with r
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