Question

find the average rate of change of ( k(x) = x + 4 ) over the interval (left-13, -10
ight). write your answer as an integer, fraction, or decimal rounded to the nearest tenth. simplify any fractions.

Explanation:

Step1: Recall the formula for average rate of change

The average rate of change of a function \( k(x) \) over the interval \([a, b]\) is given by \(\frac{k(b) - k(a)}{b - a}\). Here, \( a=-13 \) and \( b = - 10 \), and \( k(x)=x + 4 \).

Step2: Calculate \( k(-13) \) and \( k(-10) \)

For \( k(-13) \): Substitute \( x=-13 \) into \( k(x)=x + 4 \), we get \( k(-13)=-13 + 4=-9 \).
For \( k(-10) \): Substitute \( x = - 10 \) into \( k(x)=x + 4 \), we get \( k(-10)=-10 + 4=-6 \).

Step3: Substitute into the average rate of change formula

Now, substitute \( a=-13 \), \( b=-10 \), \( k(a)=-9 \) and \( k(b)=-6 \) into \(\frac{k(b)-k(a)}{b - a}\).
We have \(\frac{-6-(-9)}{-10-(-13)}=\frac{-6 + 9}{-10 + 13}=\frac{3}{3}=1\).

Answer:

\(1\)