Answer:
Domain: all real numbers except 0 and -3
Vertical asymptotes: x = 0; x = -3
Explanation:
The domain is the set of numbers that can be substituted for x.
The expression has x in the denominator. Since division by zero is undefined, x cannot have any value that would cause a zero in the denominator. To find which values of x cause a zero in the denominator, we set the denominator equal to zero and solve the equation for x.
2x^2 + 6x = 0
Factor 2x.
2x(x + 3) = 0
Divide both sides by 2.
x(x + 3) = 0
x = 0 or x + 3 = 0
x = 0 or x = -3
Since the values x = 0 and x = -3 cause the denominator to equal zero, these two values of x must be excluded from the domain.
Domain: all real numbers except 0 and -3
The vertical asymptotes happen at the x values excluded from the domain.
Vertical asymptotes: x = 0; x = -3