Question

Of these three linear functions represented below, what has the greatest rate of change?

-Function 1: y=2x+6

-Function 2:(this is a table)
x|y
-1|3
1|15
2|21

-Function 3: a number y is less than half a number x.

A) Function 3 has greatest rate of change
B) Function 2 has the greatest rate of change
C) Function 1 has the greatest rate of change
D) All three functions have the same rate of change
*would like the steps to solve this also.

Answer 1

Function 1 is 2x+6

df/dx=2 so the rate of change is 2

...

Function 2

dy/dx=21-15=6 so the rate of change is 6

....

Function 3

y<x/2, dy/dx=1/2

So Function 2 having a rate of change of 6 has the greatest rate of change.