3x x2 0

Asked by maham237 @ 21/02/2021 in Mathematics viewed by 313 People

Show all work to identify the discontinuity and zero of this function. 3x/x^2-9

Answered by maham237 @ 21/02/2021

ANSWER

Zero(s)

$x = 0$

The function is discontinuous at

$x = - 3 \:and \: x = 3$

EXPLANATION

The given rational function is

$y = \frac{3x}{ {x}^{2} - 9 }$

For this function to be equal to zero, then the numerator must be zero.

Equate the numerator to zero and solve for x.

$3x = 0$

This implies that

$x = \frac{0}{3} = 0$

The rational function is discontinuous when the denominator is equal to zero.

${x}^{2} - 9 = 0$

Solve this quadratic equation using the square root method or otherwise.

${x}^{2} = \pm \sqrt{9}$

${x} = \pm 3$

There is discontinuity at

$x = - 3 \:and \: x = 3$

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