Step1 :
Determine rate of change for each function.
For function b
x1 = 0, y1 = 0
x2 = 2, y2 = 2
[tex]\begin{gathered} \text{Rate of change = }\frac{change\text{ in y}}{\text{change in x}} \\ =\text{ }\frac{2\text{ - 0}}{2\text{ -}0} \\ =\text{ }\frac{2}{2} \\ =\text{ 1} \end{gathered}[/tex]
For function a
x1 = 0 y1 = 1
x2 = 2 y2 = 4
[tex]\begin{gathered} \text{Rate of change = }\frac{4\text{ - 1}}{2\text{ - 0}} \\ =\text{ }\frac{3}{2} \\ =\text{ 1.5} \end{gathered}[/tex]
For function c
x1 = 0 y1 = -1
x2 = 2 y2 = 0
[tex]\begin{gathered} \text{Rate of change = }\frac{0\text{ -(-1)}}{2\text{ - 0}} \\ =\text{ }\frac{1}{2} \\ =\text{ 0.5} \end{gathered}[/tex]
For function d
x1 = 0 y1 = 0.5
x2 = 2 y2 = 2.5
[tex]\begin{gathered} \text{Rate of change = }\frac{2.5\text{ - 0.5}}{2\text{ - 0}} \\ =\text{ }\frac{2}{2} \\ =\text{ 1} \end{gathered}[/tex]
Step 2: Final answer
Function a has the greatest rate of change.
