Question

1.3 rates of change in linear and quadratic func ap precalculus what is the average rate of change for each function on the 1. ( y = 7x + 10 ) on ( -6 leq x leq -4 ) 2

Explanation:

Step1: Recall average rate of change formula

The average rate of change of a function \( y = f(x) \) on the interval \([a, b]\) is given by \(\frac{f(b)-f(a)}{b - a}\). Here, \( a=-6 \), \( b = - 4 \), and \( f(x)=7x + 10 \).

Step2: Calculate \( f(-6) \) and \( f(-4) \)

For \( x=-6 \): \( f(-6)=7\times(-6)+10=-42 + 10=-32 \)
For \( x = - 4 \): \( f(-4)=7\times(-4)+10=-28 + 10=-18 \)

Step3: Apply the average rate of change formula

Substitute \( a=-6 \), \( b = - 4 \), \( f(-6)=-32 \), and \( f(-4)=-18 \) into the formula:
\[
\frac{f(-4)-f(-6)}{-4-(-6)}=\frac{-18-(-32)}{-4 + 6}=\frac{-18 + 32}{2}=\frac{14}{2}=7
\]

Answer:

7