Answer:
Part A: Function C
Part B: Function B
Step-by-step explanation:
Part A:
Initial value of function A is the value of [tex]y[/tex] at [tex]x =0[/tex].
Therefore, at [tex]x =0, y = 0[/tex]
So, initial value of function A is 0.
Initial value of function B is given as:
[tex]y=3(0)-1=0-1=-1[/tex]
Therefore, initial value of function B is -1.
Initial value of function C as seen in the graph is 2 because at [tex]x =0,y=2[/tex].
Hence, on comparing the initial values of the three functions, function C has the greatest initial value.
Part B:
Rate of change of a function is given as:
[tex]m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]
For function A, [tex](x_{1},y_{1})=(0,0)\textrm{ and }(x_{2},y_{2})=(2,5)[/tex]
Therefore, [tex]m_{A}=\frac{5-0}{2-0}=\frac{5}{2}=2.5[/tex]
For function B, the coefficient of [tex]x[/tex] represents rate of change of the function.
Therefore, rate of change of function B is [tex]m_{B}=3[/tex].
For function C, consider two points on the graph. Let the points be [tex](0,2)\textrm{ and }(3,3)[/tex]
Therefore, rate of change, [tex]m_{C}=\frac{3-2}{3-0}=\frac{1}{3}=0.33[/tex]
On comparing all the 3 rate of change, function B has the greatest rate of change of value 3.
