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Find the average rate of change of f(x)=x−4f(x) = x - 4 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 f(x)=x−4f(x) = x - 4 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 f(5)f(5) values: To find the average rate of change, we need to calculate the difference in function values divided by the difference in xx values.\newlineCalculate f(5)f(5) and f(5+h)f(5 + h):\newlinef(5)=5−4=1f(5) = 5 - 4 = 1\newlinef(5+h)=(5+h)−4=1+hf(5 + h) = (5 + h) - 4 = 1 + h
  2. Find difference in function values: Now, find the difference in function values: f(5+h)−f(5)=(1+h)−1=hf(5 + h) - f(5) = (1 + h) - 1 = h
  3. Calculate difference in x values: Calculate the difference in x values: \newlineegin{equation}(55 + h) - 55 = h\newlineegin{equation}
  4. Divide to find average rate: Now, divide the difference in function values by the difference in x values to find the average rate of change:\newlineAverage rate of change = hh=1\frac{h}{h} = 1

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