Question

1- estude os sinais das seguintes funções:

a) f(x)= 11x - 30
b) y= -3x+7
c) f(x)x/2-4
d) y= 4 - 11x

Answer 1

a) f(x)= 11x - 30

f(x) > 0 ==> 11x - 30 > 0 ==> 11x > 30 ==> x > 30/11    crescente
f(x) = 0 ==> 11x - 30 = 0 ==> 11x = 30 ==> x = 30/11    constante
f(x) < 0 ==> 11x - 30 < 0 ==> 11x < 30 ==> x < 30/11    decrescente
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b) y= -3x+7

f(x) > 0 ==> -3x + 7 > 0(-1) ==> 3x - 7 < 0 => 3x < 7 ==>x < 7/3    crescente
f(x) = 0 ==> -3x + 7 = 0(-1) ==> 3x - 7 = 0 => 3x = 7 ==>x = 7/3    constante
f(x) < 0 ==> -3x + 7 > 0(-1) ==> 3x - 7 > 0 => 3x > 7 ==>x > 7/3    decrescente
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c) f(x) = x - 4
             2
f(x) > 0 ==> x/2 - 4 > 0 ==> x - 8 > 0 ==> x > 8    crescente
f(x) = 0 ==> x/2 - 4 = 0 ==> x - 8 = 0 ==> x = 8    constante
f(x) < 0 ==> x/2 - 4 < 0 ==> x - 8 < 0 ==> x < 8    decrescente
=======================================================
d) y= 4 - 11x

f(x) > 0 ==> 4 - 11x > 0(-1) ==> 11x - 4 < 0 => 11x < 4 =>x < 4/11    crescente
f(x) = 0 ==> 4 - 11x = 0(-1) ==> 11x - 4 = 0 => 11x = 4 =>x = 4/11    constante
f(x) < 0 ==> 4 - 11x > 0(-1) => 11x - 4 > 0 => 11x > 4 =>x > 4/11   decrescente