[tex] \bf slope = m = \cfrac{rise}{run} \implies
\cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby
\begin{array}{llll}
average~rate\\
of~change
\end{array}\\\\
-------------------------------\\\\
f(x)= x^2-3 \qquad
\begin{cases}
x_1=1\\
x_2=3
\end{cases}\implies \cfrac{f(3)-f(1)}{3-1}
\\\\\\
\cfrac{[3^2-3]-[1^2-3]}{2}\implies \cfrac{6 - (-2)}{2}\implies \cfrac{6+2}{2}\implies \cfrac{8}{2}\implies 4 [/tex]
Answer: 4
Step-by-step explanation:
The given function : [tex]f(x) = x^2 - 3[/tex]
The average rate of change in a function g(x) from x=a to x=b is given by :-
[tex]k=\dfrac{g(b)-g(a)}{b-a}[/tex]
Then, the average rate of change of the given function from x = 1 to x = 3 will be :-
[tex]k=\dfrac{f(3)-f(1)}{3-1}\\\\=\dfrac{(3)^2-3-(1^2-3)}{2}=\dfrac{9-3-1+3}{2}\\\\=\dfrac{8}{2}=4[/tex]
Hence, the average rate of change of the function from x = 1 to x = 3 is 4.
