Question 1061020
I'm assuming the function is {{{f(x)=3/(x-2)}}}



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Plug in x = 4



{{{f(x)=3/(x-2)}}}



{{{f(4)=3/(4-2)}}}



{{{f(4)=3/2}}}



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Then plug in x = 7



{{{f(x)=3/(x-2)}}}



{{{f(7)=3/(7-2)}}}



{{{f(7)=3/5}}}



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Then use those values to find the average rate of change M



{{{M = (f(a)-f(b))/(a-b)}}}



{{{M = (f(4)-f(7))/(4-7)}}} Plug in a = 4 and b = 7



{{{M = (3/2-3/5)/(4-7)}}} Replace f(4) with 3/2. Replace f(7) with 3/5



{{{M = (15/10-6/10)/(4-7)}}}



{{{M = (9/10)/(-3)}}}



{{{M = (9/10)*(-1/3)}}}



{{{M = (9*(-1))/(10*3)}}}



{{{M = (-9)/(30)}}}



{{{M = -3/10}}}



So the average rate of change is {{{-3/10}}}