Question

The graph below plots a function f(x):

graph of line segment going through ordered pairs 0,150 and 3, 0

If x represents time, the average rate of change of the function f(x) in the first three seconds is ___.

Answer for Blank 1:

Answer 1

-50

Explanation:

The rate of change formula = f(b) - f(a) / b - a

f(b) = the end number (so basically 0 becuase the line ends on the point (3, 0))

f(a) = the start number (so basically 150 becuase the line starts on the point (0, 150)

b = the end time (so basically 3 becuase the line ends on the point (3, 0))

a = the start time (so basically 0 becuase the line starts on the point (0, 150)

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sorry if that is confusing... moving on...

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You would apply these numbers = 0 - 150 / 3 - 0 = -150 / 3 = -50

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This is your rate of change

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I hope this helped :)

Answer 2

The average rate of change of a linear function is the slope of the line. Since we are given the following coordinates:
(0,150) and (3,0)
We can easily solve for the slope.
m = (y2 - y1) / (x2 - x1)
m = (0 - 150) / (3 - 0) = -50

Therefore, the average rate of change of the function in the three seconds is -50.