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} =\frac{11-7}{1-0} \\ =\frac{4}{1} \end{gathered}$$\frac{15-11}{2-1}=\frac{4}{1}=4$

So the rate of change is 4.

for b(x)=2x-3

differentiate with respect to x

$\frac{db(x)}{dx}=\frac{d(2x-3)}{dx}=2$

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).