given the function defined in the table below, find the average rate of change, in simplest form, of the…

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 1 ≤ x ≤ 5.\n| x | f(x) |\n|----|----|\n| 1 | 5 |\n| 3 | 3 |\n| 5 | 9 |\n| 7 | 23 |

given the function defined in the table below, find the average rate of change, in simplest form, of the function over the interval 1 ≤ x ≤ 5.\n| x | f(x) |\n|----|----|\n| 1 | 5 |\n| 3 | 3 |\n| 5 | 9 |\n| 7 | 23 |

Answer

Explanation:

Step1: Identificar los valores de x y f(x)

Tenemos $x_1 = 1$, $f(x_1)=5$, $x_2 = 5$, $f(x_2)=9$.

Step2: Aplicar la fórmula del cambio promedio

La fórmula para el cambio promedio de una función $y = f(x)$ en el intervalo $[x_1,x_2]$ es $\frac{f(x_2)-f(x_1)}{x_2 - x_1}$. Sustituyendo los valores: $\frac{9 - 5}{5 - 1}$.

Step3: Simplificar la expresión

$\frac{9 - 5}{5 - 1}=\frac{4}{4}=1$.

Answer:

$1$