Question

Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used.

Find the average rate of change of each function over the interval [0, 2]. Match each representation with its respective average rate of change.
5
-1
4
-3
2
3
A function, f, has an
x-intercept at (2,0) and
a y-intercept at (0,-6).
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x 0 1 2 3 4
j(x) 2 0 -4 -10 -18
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Graph shows upward parabola labeled g, on coordinate plane, with vertex (minus 1, minus 4) in quadrant 3. Left slope (minus 2, minus 3) and (minus 3, 0) exits quadrant 2 at (minus 4, 5). Right slope at (minus 3, 0), (1, 0) exits quadrant 1 at (2, 5).
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Answer 1

-1: A function, f, has an x-intercept at (2,0) and a y-intercept at (0,-6).

2: 5

3: -1

4: -3

5: 4

Explanation:

The first representation describes a linear function with x-intercept at (2,0) and y-intercept at (0,-6). The average rate of change of this function over the interval [0, 2] is -1.

The second representation describes a constant function with a value of 2 at every point. The average rate of change of this function over the interval [0, 2] is 0, since the function does not change over this interval.

The third representation describes a function that increases from 1 to 9 over the interval [0, 2]. The average rate of change of this function over the interval [0, 2] is 4.

The fourth representation describes a function that decreases from 7 to -1 over the interval [0, 2]. The average rate of change of this function over the interval [0, 2] is -3.

The fifth representation describes a function that starts at 1, increases to 5, and then decreases to -3 over the interval [0, 3]. The average rate of change of this function over the interval [0, 2] is 4.