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Which function has the greater average rate over the interval [-2,-1]?x | f(x)---------2 | 10-1 | 80 | 61 | 4
g(x) = {x}^(2) - 2x + 1

Which function has the greater average rate over the interval [-2,-1]?x | f(x)---------2 | 10-1 | 80 | 61 | 4g-example-1
User AdmSteck
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1 Answer

10 votes
10 votes

First function,

F(x)

The find the greatest rate of change, you will find the slope over the given interval.

The slope of the function f(x) is m


m\text{ = }\frac{y_2-y_1_{}_{}_{}}{x_2-x_1}

From the table,

x1 = -2, y1 = 10

x2 = -1, y2 = 8


\begin{gathered} m\text{ = }\frac{8\text{ - 10}}{-1\text{ - (-2)}} \\ m\text{ = }\frac{-2}{-1\text{ + 2}} \\ m\text{ = }(-2)/(1) \\ m\text{ = -2} \end{gathered}

Second, function g(x)


\begin{gathered} g(x)=-x^2\text{ - 2x + 1} \\ whenx_1=-2,y_{1\text{ }}=-(-2)^{2\text{ }}-\text{ 2(-2) + 1 = -4 + 4 + 1 = 1} \\ \text{when x}_2=-1,y_2=-(-1)^2\text{ - 2(-1) + 1 = -1 + 2 + 1 = 2} \\ \text{next, find the rate of change} \\ m\text{ = }\frac{2\text{ - 1}}{-1\text{ -(-2)}} \\ m\text{ = }\frac{1}{-1\text{ + 2}} \\ m\text{ = }(1)/(1) \\ m\text{ = 1} \end{gathered}

Third function h(x)


\begin{gathered} \text{From the graph of h(x)} \\ \text{when x}_1=-1interceptthecurveat0,therefore.y_1\text{ = 0} \\ \text{when x}_2\text{ = -2 intercept the curve at }3,therefore,y_2\text{ = 3} \\ m\text{ = }\frac{\text{3 - 0}}{-\text{ 1 -(-2)}} \\ m\text{ = }\frac{3}{-1\text{ + 2}} \\ m\text{ = }(3)/(1) \\ m\text{ = 3} \end{gathered}

From the solution above, the function h(x) has the greatest average rate over the interval (-2, -1).

Final answer

h(x) has the greatest overage rate over interval [-2, -1]

User Porshia
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