Question

Consider the function graphed below Determine which function has the greatest rate of change over the interval (0,2)A. bB. dC. cD. a

Answer 1

Step1 :

Determine rate of change for each function.

For function b

x1 = 0, y1 = 0

x2 = 2, y2 = 2

`\begin{gathered} \text{Rate of change = }\frac{change\text{ in y}}{\text{change in x}} \\ =\text{ }\frac{2\text{ - 0}}{2\text{ -}0} \\ =\text{ }(2)/(2) \\ =\text{ 1} \end{gathered}`

For function a

x1 = 0 y1 = 1

x2 = 2 y2 = 4

`\begin{gathered} \text{Rate of change = }\frac{4\text{ - 1}}{2\text{ - 0}} \\ =\text{ }(3)/(2) \\ =\text{ 1.5} \end{gathered}`

For function c

x1 = 0 y1 = -1

x2 = 2 y2 = 0

`\begin{gathered} \text{Rate of change = }\frac{0\text{ -(-1)}}{2\text{ - 0}} \\ =\text{ }(1)/(2) \\ =\text{ 0.5} \end{gathered}`

For function d

x1 = 0 y1 = 0.5

x2 = 2 y2 = 2.5

`\begin{gathered} \text{Rate of change = }\frac{2.5\text{ - 0.5}}{2\text{ - 0}} \\ =\text{ }(2)/(2) \\ =\text{ 1} \end{gathered}`

Step 2: Final answer

Function a has the greatest rate of change.