Question

1. for ( f(x)=5x + 4 ), what is the average rate of change over ( 1,3 )?

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 \(\frac{f(b)-f(a)}{b - a}\). Here, \(a = 1\), \(b=3\), and \(f(x)=5x + 4\).

Step2: Calculate \(f(1)\) and \(f(3)\)

• For \(x = 1\): \(f(1)=5\times1+4=5 + 4=9\).
• For \(x = 3\): \(f(3)=5\times3+4=15 + 4=19\).

Step3: Substitute into the formula

\(\frac{f(3)-f(1)}{3 - 1}=\frac{19 - 9}{3-1}=\frac{10}{2}=5\).

Answer:

C. 5