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Find the average rate of change of g(x)=−8−xg(x) = -8 - x between x=4x = 4 and x=4+hx = 4 + h, where h≠0h \neq 0.\newlineSimplify your answer. Your answer may be a number or an expression in terms of hh.

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Average rate of change IIright chevron icon

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Q. Find the average rate of change of g(x)=−8−xg(x) = -8 - x between x=4x = 4 and x=4+hx = 4 + h, where h≠0h \neq 0.\newlineSimplify your answer. Your answer may be a number or an expression in terms of hh.
  1. Identify Function and Points: Identify the function and points for calculation.\newlineg(x)=−8−xg(x) = -8 - x; Calculate g(4)g(4) and g(4+h)g(4 + h).\newlineg(4)=−8−4=−12g(4) = -8 - 4 = -12.\newlineg(4+h)=−8−(4+h)=−12−hg(4 + h) = -8 - (4 + h) = -12 - h.
  2. Calculate Values: Calculate the average rate of change using the formula: (g(x2)−g(x1))/(x2−x1)(g(x_2) - g(x_1)) / (x_2 - x_1). Here, x1=4x_1 = 4 and x2=4+hx_2 = 4 + h. Average rate of change = (g(4+h)−g(4))/((4+h)−4)(g(4 + h) - g(4)) / ((4 + h) - 4). = (−12−h+12)/h(-12 - h + 12) / h. = −h/h-h / h.
  3. Average Rate of Change: Simplify the expression.\newline−hh-\frac{h}{h} simplifies to −1-1, since h≠0h \neq 0.

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