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Answer:
See Explanation
Step-by-step explanation:
The function is not properly given. So, to solve this question I'll assume it is:
f(x) = x² + 3
Required
Calculate the average rate of change on −1 ≤ x ≤ 3.
[The average rate of change (R) is calculated using:]
R = (f(b) - f(a))/(b - a)
[Where]
a ≤ x ≤ b = −1 ≤ x ≤ 3.
[This means that]
a = -1
b = 3
[Solving f(b); We have]
f(x) = x² + 3
[Substitute b for x]
f(b) = b² + 3
[Substitute 3 for b]
f(3) = 3² + 3 = 9 + 3 = 12
[Solving f(a); We have]
f(x) = x² + 3
[Substitute a for x]
f(a) = a² + 3
[Substitute -1 for b]
f(-1) = (-1)² + 3 = 1 + 3 = 4
[So, the equation becomes]
R = (f(b) - f(a))/(b - a)
R = (12 - 4)/(3 - (-1)
R = 8/(3+1)
R = 8/4
R = 2
[Hence, the average rate of change is 2]