Question

For the graphed function f(x) = (4)x − 1 + 2, calculate the average rate of change from x = 1 to x = 2.

Answer 1

Answer:

Option B is correct.

Average rate of change from x=1 to x=2 is 3

Step-by-step explanation:

Formula for Average rate of change: The ratio of the difference in the  function f(x) as it changes from a to b to the difference between a and b :

$A(x) = \frac{f(b)-f(a)}{b-a}$

As per the statement:

$f(x) = 4^{x-1} +2$

Calculate the average rate of change from x =1 to x =2

At x = 1

$f(1) = 4^{1-1} +2 = 1 +2 = 3$

At x = 2

$f(2) = 4^{2-1} +2 = 4^1 +2 = 4+2 =6$

Then;

$A(x) = \frac{f(2)-f(1)}{2-1} = \frac{6-3}{1} =\frac{3}{1} = 3$

Therefore, the average rate of change from x=1 to x=2 is 3

Answer 2

For the function
  f(x) = 4^(x-1) +2
the average rate of change on the interval [1, 2] is found by computing
  (f(2) - f(1))/(2 - 1)
  = ((4^1+2) - (4^0+2)/1
  = (6-3)
  = 3