several values of a function are given in the table.\nwhat is the average rate of change of this function…
several values of a function are given in the table.\nwhat is the average rate of change of this function between ( x = 1 ) and ( x = 3 )?
Answer
Explanation:
Step1: Recall the formula for average rate of change
The formula for the average rate of change of a function (y = f(x)) between (x=a) and (x = b) is (\frac{f(b)-f(a)}{b - a}).
Step2: Identify the values of (f(a)) and (f(b))
Here, (a = 1), (b=3). From the table, when (x = 1), (y=f(1)=-1); when (x = 3), (y = f(3)=5).
Step3: Substitute into the formula
Substitute (f(1)=-1), (f(3)=5), (a = 1), (b = 3) into (\frac{f(b)-f(a)}{b - a}). We get (\frac{5-(-1)}{3 - 1}=\frac{5 + 1}{2}=\frac{6}{2}=3).
Answer:
3