Question

Dada a função afim y= 4x+5, calcule a taxa média de variação de y em relação a x,quando este varia de:
a) 3 e 9
b) 7 e 10

Answer 1

$\\\text{Taxa m\'edia de varia\c{c}\~ao:}\\\\ \dfrac{\Delta y}{\Delta x}=\dfrac{y_2-y_1}{x_2-x_1}~~~~~(x_2\ne x_1)\\\\\\ \text{Para esta quest\~ao, temos}\\\\ y=4x+5\\\\\\ \bullet\;\;\text{Entre }x_1=3~\text{ e }~x_2=9:\\\\ y_1=4\cdot 3+5=17\\\\ y_2=4\cdot 9+5=41\\\\\\ \text{A taxa m\'edia de varia\c{c}\~ao \'e}\\\\ \dfrac{\Delta y}{\Delta x}=\dfrac{41-17}{9-3}\\\\\\ \dfrac{\Delta y}{\Delta x}=\dfrac{24}{6}\\\\\\ \boxed{\begin{array}{c}\dfrac{\Delta y}{\Delta x}=4 \end{array}}$


$\\\bullet\;\;\text{Entre }x_1=7~\text{ e }~x_2=10:\\\\ y_1=4\cdot 7+5=33\\\\ y_2=4\cdot 10+5=45\\\\\\ \text{A taxa m\'edia de varia\c{c}\~ao \'e}\\\\ \dfrac{\Delta y}{\Delta x}=\dfrac{45-33}{10-7}\\\\\\ \dfrac{\Delta y}{\Delta x}=\dfrac{12}{3}\\\\\\ \boxed{\begin{array}{c}\dfrac{\Delta y}{\Delta x}=4 \end{array}}$


Bons estudos! :-)