Rate of change of a function - HiSET
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What is the slope of the line given by the following table?
What is the slope of the line given by the following table?
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Given two points
and 
the formula for a slope is
.
Thus, since our given table is
we select two points, say
and 
and use the slope formula to compute the slop.
Thus,
.
Hence, the slope of the line generated by the table is
.
Given two points
the formula for a slope is
Thus, since our given table is
we select two points, say
and use the slope formula to compute the slop.
Thus,
Hence, the slope of the line generated by the table is
Define 
.
Give the average rate of change of 
over the interval 
.
Define 
Give the average rate of change of 
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The average rate of change of a function 
over an interval 
is equal to
Setting 
, this is
Evaluate 
and 
by substitution:
,
the correct response.
The average rate of change of a function 
Setting 
Evaluate 
the correct response.
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.
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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.
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
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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 
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 
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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.
Above is the graph of a function 
. Estimate the rate of change of 
on the interval 
Above is the graph of a function 
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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.
What is the slope of the line given by the following table?
What is the slope of the line given by the following table?
Tap to see back →
Given two points
and
the formula for a slope is
.
Thus, since our given table is
we select two points, say
and
and use the slope formula to compute the slop.
Thus,
.
Hence, the slope of the line generated by the table is
.
Given two points
the formula for a slope is
Thus, since our given table is
we select two points, say
and use the slope formula to compute the slop.
Thus,
Hence, the slope of the line generated by the table is
Define .
Give the average rate of change of over the interval .
Define
Give the average rate of change of
Tap to see back →
The average rate of change of a function over an interval is equal to
Setting , this is
Evaluate and by substitution:
,
the correct response.
The average rate of change of a function
Setting
Evaluate
the correct response.
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.
Tap to see back →
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.
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
Tap to see back →
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
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
Tap to see back →
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.
Above is the graph of a function . Estimate the rate of change of on the interval
Above is the graph of a function
Tap to see back →
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.
What is the slope of the line given by the following table?
What is the slope of the line given by the following table?
Tap to see back →
Given two points
and
the formula for a slope is
.
Thus, since our given table is
we select two points, say
and
and use the slope formula to compute the slop.
Thus,
.
Hence, the slope of the line generated by the table is
.
Given two points
the formula for a slope is
Thus, since our given table is
we select two points, say
and use the slope formula to compute the slop.
Thus,
Hence, the slope of the line generated by the table is
Define .
Give the average rate of change of over the interval .
Define
Give the average rate of change of
Tap to see back →
The average rate of change of a function over an interval is equal to
Setting , this is
Evaluate and by substitution:
,
the correct response.
The average rate of change of a function
Setting
Evaluate
the correct response.
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.
Tap to see back →
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.
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
Tap to see back →
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
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
Tap to see back →
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.
Above is the graph of a function . Estimate the rate of change of on the interval
Above is the graph of a function
Tap to see back →
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.
What is the slope of the line given by the following table?
What is the slope of the line given by the following table?
Tap to see back →
Given two points
and
the formula for a slope is
.
Thus, since our given table is
we select two points, say
and
and use the slope formula to compute the slop.
Thus,
.
Hence, the slope of the line generated by the table is
.
Given two points
the formula for a slope is
Thus, since our given table is
we select two points, say
and use the slope formula to compute the slop.
Thus,
Hence, the slope of the line generated by the table is
Define .
Give the average rate of change of over the interval .
Define
Give the average rate of change of
Tap to see back →
The average rate of change of a function over an interval is equal to
Setting , this is
Evaluate and by substitution:
,
the correct response.
The average rate of change of a function
Setting
Evaluate
the correct response.