2.Use the following graph to estimate the rate of change of the function at x=0.5 using the points (−1,−1) and (1,3)
A.The rate of change is −1/2.
B.The rate of change is 2.
C.The rate of change is 1/2.
D.The rate of change is −2.
3.The following graph shows the inches of snow on the ground over a certain number of hours. Use the graph to estimate the rate of change of the function at 3 hours using the points (0,0) and (5,10)
A.The rate of change is −1/2 of an inch per hour.
B.The rate of change is 1/2 of an inch per hour.
C.The rate of change is 2 inches per hour.
D.The rate of change is −2 inches per hour.
4.The following graph shows the average temperatures in degrees Fahrenheit (°F) over the days of a month. Use the graph to estimate the rate of change of the function at the ninth day of the month using the points (2,55) and (10,65)
A.The rate of change is 0.8 degrees Fahrenheit per day.
B.The rate of change is 1.25 degrees Fahrenheit per day.
C.The rate of change is −0.8 degrees Fahrenheit per day.
D.The rate of change is −1.25 degrees Fahrenheit per day.
5.Use the following graph to answer which of the following points would provide the most accurate estimation for the rate of change of the function as it crosses the y-axis. Explain.
(−0.5, 2)
(0.5, 3)
(−0.5, 3)
(0.5, 1)
A.(−0.5, 3) and (0.5, 1) would provide the most accurate estimation. The slope of the line drawn between these two points appears closest to the slope of the function at x=0.
B.(−0.5, 2) and (0.5, 3) would provide the most accurate estimation. The slope of the line drawn between these two points appears closest to the opposite of the slope of the function at x=0.
C.(−0.5, 2) and (0.5, 3) would provide the most accurate estimation. The slope of the line drawn between these two points appears closest to the slope of the function at x=0.
D.(−0.5, 3) and (0.5, 1) would provide the most accurate estimation. The slope of the line drawn between these two points appears closest to the opposite of the slope of the function at x=0.
Answers:
1 = C
2 = D
3 = B
4 = B
5 = D
2. To estimate the rate of change of the function at x=0.5, we need to find the slope of the line passing through the points (-1,-1) and (1,3). The slope of a line is calculated by taking the difference in y-coordinates divided by the difference in x-coordinates.
For the given points, the difference in y-coordinates is 3 - (-1) = 4, and the difference in x-coordinates is 1 - (-1) = 2.
So, the slope is 4/2 = 2.
Therefore, the rate of change of the function at x=0.5 is 2.
Answer: B. The rate of change is 2.
3. To estimate the rate of change of the function at 3 hours, we need to find the slope of the line passing through the points (0,0) and (5,10). Similar to the previous question, we calculate the slope by taking the difference in y-coordinates divided by the difference in x-coordinates.
For the given points, the difference in y-coordinates is 10 - 0 = 10, and the difference in x-coordinates is 5 - 0 = 5.
So, the slope is 10/5 = 2.
Therefore, the rate of change of the function at 3 hours is 2 inches per hour.
Answer: C. The rate of change is 2 inches per hour.
4. To estimate the rate of change of the function at the ninth day of the month, we need to find the slope of the line passing through the points (2,55) and (10,65). Again, we calculate the slope by taking the difference in y-coordinates divided by the difference in x-coordinates.
For the given points, the difference in y-coordinates is 65 - 55 = 10, and the difference in x-coordinates is 10 - 2 = 8.
So, the slope is 10/8 = 1.25.
Therefore, the rate of change of the function at the ninth day of the month is 1.25 degrees Fahrenheit per day.
Answer: B. The rate of change is 1.25 degrees Fahrenheit per day.
5. To determine which points would provide the most accurate estimation for the rate of change of the function as it crosses the y-axis, we need to consider the slope of the line drawn between the given points and compare it to the slope of the function at x=0.
Looking at the given points:
(−0.5, 2) - This point does not provide enough information about the slope.
(0.5, 3) - This point does not provide enough information about the slope.
(−0.5, 3) - This point does not provide enough information about the slope.
(0.5, 1) - This point does not provide enough information about the slope.
None of the given points provide enough information to accurately estimate the slope of the function at x=0. Therefore, none of the answer options are correct.
Answer: None of the options are correct.