Use the following graph to estimate the rate of change of the function at x=0.6 using the points(0,0) and (1,-0.5)
1.The rate of change is −0.5.
2.The rate of change is 2.
3.The rate of change is 2 inches per hour.
4.The rate of change is 1.25 degrees Fahrenheit per day.
5.(−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.
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the rate of change is the slope of the line joining the points: -1/2
Unless you are concealing some other relevant data ... ?
To estimate the rate of change of a function at a specific point using two given points on a graph, we can use the formula for the slope of a line. The slope represents the rate of change between those two points.
The slope formula is:
m = (y₂ - y₁) / (x₂ - x₁)
Using the given points (0,0) and (1,-0.5), we can substitute the values into the formula to find the slope:
m = (-0.5 - 0) / (1 - 0)
m = -0.5 / 1
m = -0.5
Therefore, the slope (rate of change) of the function between the points (0,0) and (1,-0.5) is -0.5.
Alternatively, you can visually estimate the slope by looking at the graph. In this case, you can see that the line connecting the two points is sloping downward, indicating a negative slope. By gauging the steepness of the line, you can estimate the rate of change to be about -0.5, which is consistent with the calculated value.
.1 C
.2 D
.3 A
.4 B
.5 C