Question

The graph models function R. The table of values models function S. Which statement is true about these functions?

A) The two functions have the same rate of change.
B) Both functions do not have a constant rate of change.
C) Function R has a greater rate of change than Function S.
D) Function S has a greater rate of change than Function R.

Answer 1

D: Function S has a greater rate of change than Function R.

Explanation:

Function S has a greater rate of change than Function R.

Function R → m =

rise

run

=

6

2

= 3. Function S → m =

change in y

change in x

=

31 − 21

6 − 4

=

10

2

= 5

Since 5 > 3, function S has a greater rate of change.

Answer 2

Answer: OPTION D.

Explanation:

The rate of change of a linear function is also known as "Slope".

The slope can be calculated with the following formula:

`m=(y_2-y_1)/(x_2-x_1)`

Choose two points on the function "R" graphed:

`(1,0)\\(0,-3)`

You can say that:

`y_2=-3\\y_1=0\\\\x_2=0\\x_1=1`

Substituting values into the formula, you get:

`m=(-3-0)/(0-1)=3`

Choose two point from the table that models the function "S":

`(4,21)\\(6,31)`

You can say that:

`y_2=31\\y_1=21\\\\x_2=6\\x_1=4`

Substituting values into the formula, you get:

`m=(31-21)/(6-4)=5`

Therefore, you can conclude that the function "S" has a greater rate of change than Function "R".