Question

Given the function, f(x) = x2 - 3, calculate the average rate of change of the function from x = 1 to x = 3.

Answer 1

$\bf slope = m = \cfrac{rise}{run} \implies \cfrac{ f(x_2) - f(x_1)}{ x_2 - x_1}\impliedby \begin{array}{llll} average~rate\\ of~change \end{array}\\\\ -------------------------------\\\\ f(x)= x^2-3 \qquad \begin{cases} x_1=1\\ x_2=3 \end{cases}\implies \cfrac{f(3)-f(1)}{3-1} \\\\\\ \cfrac{[3^2-3]-[1^2-3]}{2}\implies \cfrac{6 - (-2)}{2}\implies \cfrac{6+2}{2}\implies \cfrac{8}{2}\implies 4$

Answer 2

Answer: 4

Step-by-step explanation:

The given function : $f(x) = x^2 - 3$

The average rate of change in a function g(x) from x=a to x=b is given by :-

$k=\dfrac{g(b)-g(a)}{b-a}$

Then, the average rate of change of the given function from x = 1 to x = 3 will be :-

$k=\dfrac{f(3)-f(1)}{3-1}\\\\=\dfrac{(3)^2-3-(1^2-3)}{2}=\dfrac{9-3-1+3}{2}\\\\=\dfrac{8}{2}=4$

Hence, the average rate of change of the function from x = 1 to x = 3 is 4.