Problemas
Is y=8^x-6 an increasing or decreasing function? square 4 Is y=2((1)/(2))^-x+2 an increasing or decreasing function? square
Roztwór
Pedro
veterano · Tutor durante 11 años
4.2
(198 Votos)
Respuesta
Let's analyze each function separately to determine whether they are increasing or decreasing.### Function 1:
To determine if this function is increasing or decreasing, we need to look at the base of the exponential term, which is 8 in this case.- If the base of the exponential term is greater than 1, the function is increasing.- If the base of the exponential term is between 0 and 1, the function is decreasing.Since
, the function
is an increasing function.### Function 2: \( y = 2 \left( \frac{1}{2} \right)^{-x} + 2 \)First, let's rewrite the function for clarity:
Now, let's analyze the base of the exponential term, which is
.- If the base of the exponential term is greater than 1, the function is increasing.- If the base of the exponential term is between 0 and 1, the function is decreasing.Since
, the function
is an increasing function.### Summary- The function
is an increasing function.- The function \( y = 2 \left( \frac{1}{2} \right)^{-x} + 2 \) is an increasing function.So, the answers are:1.
is an increasing function.2. \( y = 2 \left( \frac{1}{2} \right)^{-x} + 2 \) is an increasing function.