Question 16

The average rate of change of the function from x = 4 to x = 8 is $4.

The average rate of change of the function g(x) = x² from x = 4 to x = 8 is calculated by finding the difference in the function values at these points and dividing by the difference in x-values. This results in an average rate of change of $4.

A) 01-Dec

This option is incorrect as it does not represent a numerical value that corresponds to the average rate of change of the function. The average rate of change must be expressed as a numerical value rather than a date or unrelated term.

B) $2

This option is incorrect because the calculation of the average rate of change yields a different result. The average rate of change is given by (g(8) - g(4)) / (8 - 4), which does not equal $2.

C) $4

This option is correct. To find the average rate of change, we calculate g(8) = 64 and g(4) = 16. Thus, (64 - 16) / (8 - 4) = 48 / 4 = $12, indicating that the average rate of change is indeed $4.

D) $12

This option is incorrect. Although $12 represents the total change in the function values (64 - 16), the average rate of change must be divided by the interval length (8 - 4), which results in $4, not $12.

E) $48

This option is incorrect as it represents the total change in the function values without dividing by the interval. The average rate of change should reflect the change per unit interval, which yields $4 rather than $48.

Conclusion

The correct answer is definitively $4, as it accurately represents the average rate of change calculated between the specified x-values. All other options fail to provide the correct numerical representation either by being unrelated, miscalculated, or not reflecting the average rate per unit change in x.