Question

Which function has a greater rate of change? Function A: x 1.5 2.5 3.5 4.5 5.5 y 5 0 –5 –10 –15 Function B: y = –4.5x + 15 Function A has a rate of change of –5 and Function B has a rate of change of –4.5, so Function A has a greater rate of change. Function A has a rate of change of 5 and Function B has a rate of change of 4.5, so Function A has a greater rate of change. Function A has a rate of change of 5 and Function B has a rate of change of 4.5, so Function B has a greater rate of change. Function A has a rate of change of –5 and Function B has a rate of change of –4.5, so Function B has a greater rate of

Answer 1

Function A has a rate of change of -5 and Function B has a rate of change of -4.5, so Function B has a greater rate of

Explanation:

Function A:

`\begin{array}{cccccc}x & {1.5} & {2.5} & {3.5} & {4.5} & {5.5} \ \\ y & {5} & {0} & {-5} & {-10} & {-15} \ \end{array}`

Function B:

`y = -4.5x + 15`

Required

Which has a greater rate of change

The rate of change of function A is calculated as thus:

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

Where:

`(x_1,y_1) = (1.5,5)`

`(x_2,y_2) = (2.5,0)`

So, we have:

`m = (0-5)/(2.5 - 1.5)`

`m = (-5)/(1)`

`m = -5`

For function B

The general function is:

`y = mx + b`

Where

m is the rate of change

By comparing
`y = mx + b` to
`y = -4.5x + 15`

`m = -4.5`

So, we have that:

Function A has a rate of -5; function B has a rate of -4.5.

By comparison: -4.5 is greater than 5

Hence, function B has a greater rate.