Question

Does Function A or Function B have a greater rate of change over the Interval x=2 to x-47 Justify and explain your choice. (Do you like that they can't see the point (4,?) in the graph? If not you can change the interval to x-1 to x=3)

Answer 1

Function B

Explanation:

The average rate of change of function f(x) over the interval a ≤ x ≤ b is given by:

`(f(b)-f(a))/(b-a)`

Given interval: 2 ≤ x ≤ 4

Therefore: a = 2 and b = 4

Function A

From inspection of the given table:

• f(2) = -4
• f(4) = 6

Substituting these values into the formula:

`\implies \textsf{Average rate of change}=(f(4)-f(2))/(4-2)=(6-(-4))/(2)=5`

Function B

Given function:
`y=2^x+1`

`\implies f(2)=2^2+1=5`

`\implies f(4)=2^4+1=17`

Substituting these values into the formula:

`\implies \textsf{Average rate of change}=(f(4)-f(2))/(4-2)=(17-5)/(2)=6`

As 6 > 5, function B has a greater rate of change over the interval 2 ≤ x ≤ 4

Answer 2

• Function B

Explanation:

Function A

• x = 2 ⇒ y = - 4
• x = 4 ⇒ y = 6

Rate of change

• (6 - (-4))/(4 - 2) = 10/2 = 5

Function B

• x = 2 ⇒ y = 2² + 1 = 5
• x = 4 ⇒ y = 2⁴ + 1 = 17

Rate of change

• (17 - 5)/(4 - 2) = 12/2 = 6

Since 6 > 5, the function B has greater rate of change in the given interval