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| Section | Objectives |
|---|---|
| Polynomial and Rational Expressions | - Rational Expressions
|
| Foundations of Algebra | - Equations and Inequalities
|
| Exponential and Logarithmic Concepts | - Logarithmic Basics
|
| Functions and Graphs | - Graphing Functions
|
| Linear Functions and Systems | - Linear Equations
|
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NEW QUESTION # 55
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: C
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 # 56
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: C
Explanation:
This question asks which town's population is growing at a faster rate.
Since both population graphs are straight lines, we compare their slopes.
The slope of a line represents the rate of change:
" slope " = " change in population " / " change in time "
From the graph:
Town A starts at about 8.0thousand people and increases at a rate of about 1.0thousand people per year.
Town B starts at about 5.5thousand people and increases at a rate of about 1.3thousand people per year.
Even though Town A starts with a larger population, the question asks about the growth rate, not the starting population.
Compare the rates:
1.3 > 1.0
So Town B is growing faster than Town A.
NEW QUESTION # 57
A coach is placing an order for team shirts. The graph shows the total cost based on the number of shirts.
What is the cost of each additional shirt?
Exhibit:
Answer: D
Explanation:
This question asks for the cost of each additional shirt, which is the slope of the linear graph. The slope tells how much the total cost increases for each increase of 1 shirt. From the exhibit, the graph shows a starting cost near $39 and a point near (10, 139). The increase in cost from 0 shirts to 10 shirts is 139#39=100 dollars.
Dividing by 10 shirts gives a rate of 10 dollars per shirt. The fixed starting cost is not the cost of a shirt; it is the initial fee or setup cost. Since the graph rises by $10 for each additional shirt, the cost per additional shirt is $10.00. Therefore, the answer is B.
NEW QUESTION # 58
The graphed function n(t)represents the number of people, n, at a park thours after 8:00 a.m. The plotted points Aand Bhave coordinates (2#110)and (6#182).
Which statement gives the correct interpretation of the average rate of change of the number of people over the interval from point Ato point B?
Answer: C
Explanation:
The average rate of change measures how much the output changes per one unit of input.
Here:
t= " hours after 8:00 a.m. "
and
n(t)= " number of people at the park "
The two given points are:
A=(2,110)
and
B=(6,182)
This means:
At t=2hours after 8:00 a.m., there were 110people at the park.
At t=6hours after 8:00 a.m., there were 182people at the park.
Now calculate the average rate of change:
" Average rate of change " =(182-110)/(6-2)
=72/4
=18
Because the value is positive, the number of people is increasing.
So the correct interpretation is:
" The number of people at the park increases at an average rate of 18 people per hour. "
NEW QUESTION # 59
A researcher collected data on the number of large donations per year to a charitable organization. The results are shown in the scatterplot. A regression function is graphed with r