13. what is the average rate of change for $f(x)=x^{2}-2x + 3$ over $2,5$? a. 5 b. 3 c. 4 d. 6

Explanation:

Step1: Recall the formula for average rate of change

The formula for the average rate of change of a function (y = f(x)) over the interval ([a,b]) is (\frac{f(b)-f(a)}{b - a}).

Step2: Find (f(2)) and (f(5))

Given (f(x)=x^{2}-2x + 3). For (x = 2): (f(2)=2^{2}-2\times2 + 3=4-4 + 3=3). For (x = 5): (f(5)=5^{2}-2\times5+3=25 - 10+3=18).

Step3: Calculate the average rate of change

Using the formula (\frac{f(b)-f(a)}{b - a}), with (a = 2), (b = 5), (f(a)=3), (f(b)=18). (\frac{f(5)-f(2)}{5 - 2}=\frac{18 - 3}{3}=\frac{15}{3}=5).

Answer:

a. 5