Question

1. 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