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Find the average rate of change of g(x)=x+15g(x) = x + 15 between x=−5x = -5 and x=−5+hx = -5 + 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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Q. Find the average rate of change of g(x)=x+15g(x) = x + 15 between x=−5x = -5 and x=−5+hx = -5 + h, where h≠0h \neq 0.\newlineSimplify your answer. Your answer may be a number or an expression in terms of hh.
  1. Calculate g(x)g(x): Calculate g(x)g(x) at the initial point x=−5x = -5.\newlineg(−5)=−5+15=10g(-5) = -5 + 15 = 10
  2. Calculate g(x)g(x): Calculate g(x)g(x) at the point x=−5+hx = -5 + h.\newlineg(−5+h)=(−5+h)+15=h+10g(-5 + h) = (-5 + h) + 15 = h + 10
  3. Find change: Find the change in g(x)g(x) over the change in xx.
    Change in g(x)g(x) = g(−5+h)−g(−5)=(h+10)−10=hg(-5 + h) - g(-5) = (h + 10) - 10 = h
    Change in xx = (−5+h)−(−5)=h(-5 + h) - (-5) = h
  4. Calculate average rate: Calculate the average rate of change.\newlineAverage rate of change = Change in g(x)Change in x\frac{\text{Change in } g(x)}{\text{Change in } x} = hh\frac{h}{h} = 11

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