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.
No graphs here, but the rate of change, or slope, between two points
(x1,y1) and (x2,y2) is always
(y2-y1)/(x2-x1)
So plug in the numbers you have been given, and you can answer the questions.
2. To find the rate of change of the function at x=0.5, we can use the formula:
Rate of Change = (y2 - y1) / (x2 - x1)
Given the points (-1, -1) and (1, 3), we can substitute these values into the formula:
Rate of Change = (3 - (-1)) / (1 - (-1))
Rate of Change = (3 + 1) / (1 + 1)
Rate of Change = 4 / 2
Rate of Change = 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 find the rate of change of the function at 3 hours, we can use the formula:
Rate of Change = (y2 - y1) / (x2 - x1)
Given the points (0, 0) and (5, 10), we can substitute these values into the formula:
Rate of Change = (10 - 0) / (5 - 0)
Rate of Change = 10 / 5
Rate of Change = 2
Therefore, the rate of change of the function at 3 hours is 2.
Answer: C. The rate of change is 2 inches per hour.
4. To find the rate of change of the function at the ninth day of the month, we can use the formula:
Rate of Change = (y2 - y1) / (x2 - x1)
Given the points (2, 55) and (10, 65), we can substitute these values into the formula:
Rate of Change = (65 - 55) / (10 - 2)
Rate of Change = 10 / 8
Rate of Change = 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 estimate the rate of change of the function as it crosses the y-axis, we need to find two points that are very close to x=0 on the graph.
Looking at the given points, we can see that (-0.5, 3) and (0.5, 1) are the closest to x=0. We can draw a line passing through these two points and observe its slope.
By visually inspecting the graph, we can see that the slope of the line passing through (-0.5, 3) and (0.5, 1) appears closest to the slope of the function at x=0.
Therefore, the most accurate estimation for the rate of change of the function as it crosses the y-axis would be (−0.5, 3) and (0.5, 1).
Answer: 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.
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 formula for slope is (change in y)/(change in x).
The change in y is 3 - (-1) = 4, and the change in x 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.
The correct answer is B.
3. To estimate the rate of change at 3 hours, we need to find the slope of the line passing through the points (0,0) and (5,10).
The change in y is 10 - 0 = 10, and the change in x 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.
The correct answer is C.
4. To estimate the rate of change at the ninth day, we need to find the slope of the line passing through the points (2,55) and (10,65).
The change in y is 65 - 55 = 10, and the change in x is 10 - 2 = 8.
So, the slope is 10/8 = 1.25.
Therefore, the rate of change of the function at the ninth day is 1.25 degrees Fahrenheit per day.
The correct answer is B.
5. To estimate the rate of change as the function crosses the y-axis, we need to look at the points (-0.5, 2) and (0.5, 3). We want to find the points that provide the most accurate estimation of the slope of the function at x=0.
Looking at the graph, it appears that the slope of the function at x=0 is closer to the slope of the line passing through the points (-0.5, 3) and (0.5, 1). This is because the line is steeper and matches the direction of the function at that point.
Therefore, the correct answer is D. (−0.5, 3) and (0.5, 1) would provide the most accurate estimation.