Question

Which linear function has the greatest initial value and change.

Answer 1

c and b

Explanation:

i did the question

Answer 2

Part A: Function C

Part B: Function B

Explanation:

Part A:

Initial value of function A is the value of
`y` at
`x =0`.

Therefore, at
`x =0, y = 0`

So, initial value of function A is 0.

Initial value of function B is given as:

`y=3(0)-1=0-1=-1`

Therefore, initial value of function B is -1.

Initial value of function C as seen in the graph is 2 because at
`x =0,y=2`.

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:

`m=(y_(2)-y_(1))/(x_(2)-x_(1))`

For function A,
`(x_(1),y_(1))=(0,0)\textrm{ and }(x_(2),y_(2))=(2,5)`

Therefore,
`m_(A)=(5-0)/(2-0)=(5)/(2)=2.5`

For function B, the coefficient of
`x` represents rate of change of the function.

Therefore, rate of change of function B is
`m_(B)=3`.

For function C, consider two points on the graph. Let the points be
`(0,2)\textrm{ and }(3,3)`

Therefore, rate of change,
`m_(C)=(3-2)/(3-0)=(1)/(3)=0.33`

On comparing all the 3 rate of change, function B has the greatest rate of change of value 3.