Estimate rate of change from a graph - HiSet: High School Equivalency Test: Math
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The graph of a function is given above, with the coordinates of two points on the curve shown. Use the coordinates given to approximate the rate of change of the function between the two points.
The graph of a function is given above, with the coordinates of two points on the curve shown. Use the coordinates given to approximate the rate of change of the function between the two points.
The rate of change between two points on a curve can be approximated by calculating the change between two points.
Let 
be the coordinates of the first point and 
be the coordinates of the second point. Then the formula giving approximate rate of change is:
Notice that the numerator is the overall change in y, and the denominator is the overall change in x.
The calculation for the problem proceeds as follows:
Let 
be the first point and 
be the second point. Substitute in the values from these coordinates:
Subtract to get the final answer:
Note that it does not matter which you assign to be the first point and which you assign to be the second, as it will lead to the same value due to negatives canceling out.
The rate of change between two points on a curve can be approximated by calculating the change between two points.
Let
Notice that the numerator is the overall change in y, and the denominator is the overall change in x.
The calculation for the problem proceeds as follows:
Let
Subtract to get the final answer:
Note that it does not matter which you assign to be the first point and which you assign to be the second, as it will lead to the same value due to negatives canceling out.
Compare your answer with the correct one above
Above is the graph of a function
. The average rate of change of 
over the interval 
is 
. Which of these values comes closest to being a possible value of 
?
Above is the graph of a function
The average rate of change of a function 
on the interval 
is equal to
.
Restated, it is the slope of the line that passes through 
and 
.
To find the correct value of 
that answers this question, it suffices to examine the line with slope 
through 
and find the point among those given that is closest to the line. This line falls 4 units for every 5 horizontal units, so the line looks like this:
The 
-coordinate of the point of intersection is closer to 2 than to any other of the values in the other four choices. This makes 2 the correct choice.
The average rate of change of a function 
Restated, it is the slope of the line that passes through 
To find the correct value of 
The 
Compare your answer with the correct one above
Above is the graph of a function 
, which is defined and continuous on 
. The average rate of change of 
on the interval 
is 4. Estimate 
.
Above is the graph of a function 
The rate of change of a function 
on the interval 
is equal to
.
Set 
. Examine the figure below:
The graph passes through the point 
, so 
. Therefore,
and, substituting,
Solve for 
using algebra:
,
the correct response.
The rate of change of a function
Set 
The graph passes through the point 
and, substituting,
Solve for 
the correct response.
Compare your answer with the correct one above
Above is the graph of a function 
. Estimate the rate of change of 
on the interval 
Above is the graph of a function 
The rate of change of a function on the interval is equal to
.
Set 
. Refer to the graph of the function below:
The graph passes through 
and 
.
. Thus,
,
the correct response.
The rate of change of a function
Set 
The graph passes through 
the correct response.
Compare your answer with the correct one above