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Consider the functions graphed below. A curve a intersects a parabola b at (negative 1, 0 point 5) and a parabola c at (negative 2 point 4, 0 point 3). A diagonal curve d intersects the parabola b at (0 point 5, 0) and (2, 3) and parabola c at (negative 1 point 2, negative 1 point 2). Determine which function has the greatest rate of change over the interval [0, 2]. A. d B. b C. c D. a

In Mathematics, the rate of change of a function over a given interval can be determined by calculating the slope of the straight line which connect its end points.

Mathematically, the slope of any straight line can be calculated by using this formula;

[tex]Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}[/tex]

For line a, we have:

Points (x, y) = (0, 1) and (2, 4)

Slope = (4 - 1)/(2 - 0)

Slope = 3/2 or 1.5.

For line b, we have:

Points (x, y) = (0, 0) and (2, 2)

Slope = (2 - 0)/(2 - 0)

Slope = 2/2 or 1.0.

For line c, we have:

Points (x, y) = (0, -1) and (2, 0)

Slope = (0 + 1)/(2 - 0)

Slope = 1/2 or 0.5.

For line d, we have:

Points (x, y) = (0, 0.5) and (2, 2.5)

Slope = (2.5 - 0.5)/(2 - 0)

Slope = 2/2 or 1.

In conclusion, we can logically deduce that "function a" has the greatest rate of change over the interval [0, 2].

Read more on slope here: https://brainly.com/question/10064802

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