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Use the graph to determine which one of the three statements below is a lie.

The average rate of change between [0,4] is positive
The average rate of change between [-3, 4] is 7.
The average rate of change between [0,4] is ¾.

Explain using one or two sentences why it is a lie or how to make it a true statement.

Use The Graph To Determine Which One Of The Three Statements Below Is A Lie The Average Rate Of Change Between 04 Is Positive The Average Rate Of Change Between class=

Sagot :

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Answer:

Step-by-step explanation:

One formula for "average rate of change" is

               f(b) - f(a)

a. r. c. = -------------------  = (increase in y) / (increase in x

                   b - a

In the case of this particular function, a = 0, b = 4, and the related y-values are f(a) = f(0) = -3, f(b) = f(4) = 0, and so the average rate of change of this function on (0, 4) is

               f(4) - f(0)          0 - (-3)

a. r. c. = ---------------- = --------------- = +3/4

                   4 - 0                  4

Therefore, "The average rate of change between [0,4] is positive" is true.

               

               f(4) - f(-3)          0 - (0)

a. r. c. = ---------------- = --------------- = 0 (not 7)

                   4 - 0                  4

Therefore, "The average rate of change between [-3,4] is positive" is false.  The average r. of c. is actually 0.  (Again, see above).

From above,

               f(4) - f(0)          0 - (-3)

a. r. c. = ---------------- = --------------- = +3/4    This is true

                   4 - 0                  4

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