SOLUTION: Please, help me solving it... Use interval notation to write the domain of f: f(x)= x-1\3x + 6

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.

RELATED QUESTIONS
Please help me solve this problem: Find the domain and range of the function. Use... (answered by solver91311)

find the domain of f and write it in interval notation. f(x)=... (answered by MathLover1)

Write the domain of the ration function in interval notation. F(x)= 1/x-10 I just... (answered by stanbon)

SOMEONE PLEASE HELP ME WITH THIS PROBLEM: IF f(x)=x(x+3)(x-1), use interval notation to... (answered by Nate)

Please help me solve this problem: the direction are as follow: Find the domain of the... (answered by stanbon)

f(x) = 1/ 3x + 2, find the domain of the rational function and write the answer in... (answered by lwsshak3)

Graph f as a solid line and F-1 as a dashed line in the same rectangular coordinate... (answered by CPhill)

Find the domain of the function and express the answer in interval notation. f(x)=3x-1.... (answered by nerdybill)

find the domain of f(x)=7+ sqrt (3x+21), and express it using interval notation. (answered by stanbon)