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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)

Does Function A or Function B have a greater rate of change over the Interval x2 to x47 Justify and explain your choice Do you like that they cant see the point class=

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mhanifa

Answer:

  • Function B

Step-by-step 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

semsee45

Answer:

Function B

Step-by-step explanation:

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

  [tex]\dfrac{f(b)-f(a)}{b-a}[/tex]

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:

[tex]\implies \textsf{Average rate of change}=\dfrac{f(4)-f(2)}{4-2}=\dfrac{6-(-4)}{2}=5[/tex]

Function B

Given function: [tex]y=2^x+1[/tex]

[tex]\implies f(2)=2^2+1=5[/tex]

[tex]\implies f(4)=2^4+1=17[/tex]

Substituting these values into the formula:

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

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

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