Question

Faça o estudo do sinal das funções.

a)y= 3x-7
b)y= 2-4x
c)y= -4x
d)y= 3x/2

Answer 1

a)y= 3x-7

a) f(x)> 0 ==> 3x - 7  > 0 ==>  3x > 7 ==> x > 7/3

b) f(x)= 0 ==> 3x - 7  = 0 ==>  3x = 7 ==> x = 7/3

c) f(x)< 0 ==>3x - 7  < 0 ==>  3x < 7 ==> x < 7/3
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b)y= 2-4x

a) f(x)> 0 ==> 2 - 4x > 0 ==> -4x > -2(-1) ==> 4x < 2 ==> x < 2/4

b) f(x)= 0 ==>  2 - 4x = 0 ==> -4x = -2(-1) ==> 4x = 2 ==> x = 2/4

c) f(x)< 0 ==>  2 - 4x < 0 ==> -4x < -2(-1) ==> 4x > 2 ==> x > 2/4
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c)y= -4x

a) f(x)> 0 ==> - 4x > 0 ==> -4x > 0(-1) ==> x < 0/4 ==> x < 0

b) f(x)= 0 ==> - 4x = 0 ==> -4x = 0(-1) ==> x = 0/4 ==> x = 0

c) f(x)< 0 ==> - 4x < 0 ==> -4x < 0(-1) ==> x > 0/4 ==> x > 0  ====================================================
d)y= 3x/2
a) f(x)> 0 ==> 3x/2 > 0 ==>  3x > 0 ==> x > 0

b) f(x)= 0 ==> 3x/2  = 0 ==>  3x = 0 ==> x = 0

c) f(x)< 0 ==>3x/2  < 0 ==>  3x < 0 ==> x < 0