Question

2. (Proficient/Distinguished) Find THE RATE OF CHANGE over the interval [0, 2]for the table a(x), the function b(x) and the graph c(x) below. Then order themfrom least to greatest. MAKE SURE YOU SHOW YOUR WORK, AND EXPLAIN YOURTHINKING. Choose this number 2 if you want to type your answer.

Answer 1

the value of ax corresponds to the interval (0,2) is given as follows

at 0 it is 7, at 1 it is 11 and at 2 it is 15

the rate of the change will be the ratio of the change in ax values to the change in the x values

`\begin{gathered} =(11-7)/(1-0) \\ =(4)/(1) \end{gathered}`
`(15-11)/(2-1)=(4)/(1)=4`

So the rate of change is 4.

for b(x)=2x-3

differentiate with respect to x

`(db(x))/(dx)=(d(2x-3))/(dx)=2`

so the rate of change is 2 .

For C(x) the rate of change will equal to the gradient of the line

so the rate of chage is m=b/a=3/2 =1.5

b is the length of the line of the section on y axis . and a is the length of the section on x-axis.

it is equal to tan value of the triangle. made by the line.

So the order from least to greatest is c(x)< b(x) < a(x).