the average rate of change of ( g(x) ) between ( x = 4 ) and ( x = 7 ) is ( \frac{5}{6} ). which statement…

the average rate of change of ( g(x) ) between ( x = 4 ) and ( x = 7 ) is ( \frac{5}{6} ). which statement must be true?\n( g(7)-g(4)=\frac{5}{6} )\n( \frac{g(7 - 4)}{7 - 4}=\frac{5}{6} )\n( \frac{g(7)-g(4)}{7 - 4}=\frac{5}{6} )\n( \frac{g(7)}{g(4)}=\frac{5}{6} )

the average rate of change of ( g(x) ) between ( x = 4 ) and ( x = 7 ) is ( \frac{5}{6} ). which statement must be true?\n( g(7)-g(4)=\frac{5}{6} )\n( \frac{g(7 - 4)}{7 - 4}=\frac{5}{6} )\n( \frac{g(7)-g(4)}{7 - 4}=\frac{5}{6} )\n( \frac{g(7)}{g(4)}=\frac{5}{6} )

Answer

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function (y = g(x)) over the interval ([a,b]) is given by (\frac{g(b)-g(a)}{b - a}). Here, (a = 4) and (b=7).

Step2: Substitute the values into the formula

Substituting (a = 4) and (b = 7) into the formula (\frac{g(b)-g(a)}{b - a}), we get (\frac{g(7)-g(4)}{7 - 4}). Since the average rate of change is (\frac{5}{6}), we have (\frac{g(7)-g(4)}{7 - 4}=\frac{5}{6}).

Answer:

(\frac{g(7)-g(4)}{7 - 4}=\frac{5}{6}) (the third option)