Question

The average rate of change of g(x) between x=4 and x=7 is 5/6. Which statement must be true?

A) g(7)-g(4)=5/6

B) g(7-4)/7-4=5/6

C) g(7)-g(4)/7-4=5/6

D) g(7)/g(4)=5/6

Answer 1

Choice C)

`\displaystyle (g(7) - g(4))/(7 - 4) = (5)/(6)`.

Explanation:

The average rate of change of a function is:

`\displaystyle \frac{\text{Change in Function Value}}{\text{Change in Independent Variable}}`.

Note that
`\text{Change} = \text{Final Value} - \text{Initial Value}`.

For this question,

• Initial Independent Variable value: 4;
• Final Independent Variable value: 7.

As a result,

• Change in Independent Variable value:
  `7 - 4`.

• Initial function value: g(4);
• Final function value: g(7).

As a result,

• Change in function value:
  `g(7) - g(4)`.

The average rate of change in the value of
`g(x)` between
`x = 4` and
`x = 7` will be:

`\displaystyle (g(7)-g(4))/(7 - 4)`.