Questions: Based on the graphs of f(x) and g(x) below, answer the following questions. You should not approximate any of your answers. a) What is the average rate of change of f(x) over the interval 2.2 ≤ x ≤ 4 ? b) What is the average rate of change of g(x) over the interval 2.2 ≤ x ≤ 6.1 ?

Solution Steps

• From the graph, determine the values of \( f(x) \) at \( x = 2.2 \) and \( x = 4 \).
• \( f(2.2) = 2.9 \)
• \( f(4) = 2.9 \)

• Use the formula for the average rate of change: \(\frac{f(b) - f(a)}{b - a}\)
• Here, \( a = 2.2 \) and \( b = 4 \)
• \(\frac{f(4) - f(2.2)}{4 - 2.2} = \frac{2.9 - 2.9}{4 - 2.2} = \frac{0}{1.8} = 0\)

• From the graph, determine the values of \( g(x) \) at \( x = 2.2 \) and \( x = 6.1 \).
• \( g(2.2) = 2.9 \)
• \( g(6.1) = 4.9 \)

• Use the formula for the average rate of change: \(\frac{g(b) - g(a)}{b - a}\)
• Here, \( a = 2.2 \) and \( b = 6.1 \)
• \(\frac{g(6.1) - g(2.2)}{6.1 - 2.2} = \frac{4.9 - 2.9}{6.1 - 2.2} = \frac{2}{3.9} \approx 0.513\)

Final Answer