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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

Respuesta :

jacob193

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].

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