Question

Which linear function has the greatest initial value and change.

Answer 1

Answer:

Part A: Function C

Part B: Function B

Step-by-step 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:

$m=\frac{y_{2}-y_{1}}{x_{2}-x_{1}}$

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

Therefore, $m_{A}=\frac{5-0}{2-0}=\frac{5}{2}=2.5$

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, $m_{C}=\frac{3-2}{3-0}=\frac{1}{3}=0.33$

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