Faça o estudo do sinal da função y = 3x+9 e indique para que valores de x a função é positiva, negativa ou nula:
a) positiva x>3, negativa x<3 e nula x=3
b) positiva x>-3, negativa x<-3 e nula x=-3
c) positiva x<3, negativa x>3 e nula x=3
d) positiva x<-3, negativa x>-3 e nula x=-3

Correct option: b)

Step-by-step explanation:

To study the sign of the function, we have 3 cases:

Positive function: y>0

Negative function: y<0

Null function: y=0

Then, we just need to use the value of y in these inequations (or equation in the last case) to find the values of x:

Positive function: 3x + 9 > 0 -> 3x > -9 -> x > -3

Positive function: 3x + 9 < 0 -> 3x < -9 -> x < -3

Positive function: 3x + 9 = 0 -> 3x = -9 -> x = -3

Correct option: b)