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

Answer:Choice C)[tex]\displaystyle \frac{g(7) - g(4)}{7 - 4} = \frac{5}{6}[/tex].Step-by-step explanation:The average rate of change of a function is:[tex]\displaystyle \frac{\text{Change in Function Value}}{\text{Change in Independent Variable}}[/tex].Note that [tex]\text{Change} = \text{Final Value} - \text{Initial Value}[/tex].For this question,Initial Independent Variable value: 4;Final Independent Variable value: 7.As a result,Change in Independent Variable value: [tex]7 - 4[/tex].Initial function value: g(4);Final function value: g(7).As a result,Change in function value: [tex]g(7) - g(4)[/tex].The average rate of change in the value of [tex]g(x)[/tex] between [tex]x = 4[/tex] and [tex]x = 7[/tex] will be:[tex]\displaystyle \frac{g(7)-g(4)}{7 - 4}[/tex].