The average rate of change of g(x) over the interval 1 ≤ x ≤ 4 is 27. What is the missing value in the table? x |0 | 1 | 2 | 3 | 4
g(x)|0 |3| 6 | 15| ?

The value of g(x) ar x = 4 is 84.

i.e. g(4) = 84

Step-by-step explanation:

Given the table

x             0             1             2             3             4

g(x)        0             3             6             15          BLANK

The average rate of change of g(x) over the interval 1 ≤ x ≤ 4 is 27.

at x₁ = 1, g(x₁) = 3

at x₂ = 4,  g(x₂) = g(4) = ?

The average rate of change = 27

Using the formula involving the average rate of change  

Average rate = [g(x₂) - g(x₁)] / [ x₂ - x₁]

substituting x₁ = 1, g(x₁) = 3, x₂ = 4 and Average rate = 27  

                  27  = [g(4)  - 3] / [4 - 1]

                   27 = [g(4)  - 3] / [3]

                27×3 = g(4)  - 3

                  81   = g(4)  - 3

              81+3   = g(4)

                  84 = g(4)

Thus,

The value of g(x) ar x = 4 is 84.

i.e. g(4) = 84

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thus, the first answer choice, y = sec x, is the correct one