Question 505848: Please, help me solving it...
Use interval notation to write the domain of f:
f(x)= x-1\3x + 6
Answer by Theo(13342)   (Show Source):
You can put this solution on YOUR website! (x-1) / (3x+6)
the denominator will be 0 when x = -2.
the domain will be all real values of x except x = -2.
this would show up as:
(-infinity,-2) union (-2,infinity)
this reads:
x is smaller than -2, or x is greater than -2, but x is not equal to -2.
a graph of this equation is shown below:
you can see that, at x = -2, there is a vertical asymptote.
as x approaches -2 from the left side, the value of y approaches minus infinity.
as x approaches -2 from the right side, the value of y approaches infinity.
x can never be equal to -2 because y can never be equal to infinity because infinity is not a number.
the domain of the equation is represented by the value of x.
the range of the equation is represented by the value of y.
the value in the domain has to lead to a real value in the range.
while -2 is a real value, it cannot lead to a real value in the range because the value of anything divided by 0 is undefined.
when x = -2, the value of the denominator becomes 3*(-2) + 6 which which becomes 6 - 6 which equals 0.
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