ANSWER
Zero(s)
[tex]x = 0[/tex]
The function is discontinuous at
[tex]x = - 3 \:and \: x = 3[/tex]
EXPLANATION
The given rational function is
[tex] y = \frac{3x}{ {x}^{2} - 9 } [/tex]
For this function to be equal to zero, then the numerator must be zero.
Equate the numerator to zero and solve for x.
[tex]3x = 0[/tex]
This implies that
[tex]x = \frac{0}{3} = 0[/tex]
The rational function is discontinuous when the denominator is equal to zero.
[tex] {x}^{2} - 9 = 0[/tex]
Solve this quadratic equation using the square root method or otherwise.
[tex] {x}^{2} = \pm \sqrt{9} [/tex]
[tex]{x} = \pm 3[/tex]
There is discontinuity at
[tex]x = - 3 \:and \: x = 3[/tex]
