MHB Where is the Vertical Asymptote of f(x) = (5 - x^2)/(x - 3)?

[mathdad]

Find the vertical asymptote of f(x) = (5 - x^2)/(x - 3). I need the steps not the solution.

 

[skeeter]

Vertical asymptote is x = 3 ... why?

 

[tkhunny]

Find the vertical asymptote of f(x) = (5 - x^2)/(x - 3). I need the steps not the solution.

$g(x) = \dfrac{9-x^{2}}{x-3}$

NOT a Vertical Asymptote. Why?

 

[mathdad]

Vertical asymptote is x = 3 ... why?

At x = 3, the denominator of the function has a zero and becomes undefined.

Can we also say there is discontinuity at x = 3?

 

[mathdad]

$g(x) = \dfrac{9-x^{2}}{x-3}$

NOT a Vertical Asymptote. Why?

According to Skeeter, x = 3 is a vertical asymptote.

Let f be a function.

Let g be a function.

Correct me if I am wrong.

Say we have a rational function y = f/g.

If y = 0/g, is this also discontinuity or does discontinuity apply only when the denominator of a function is 0?

If y = f/0, is this a vertical asymptote?

Are the words discontinuity and vertical asymptote related?

 

[skeeter]

$g(x) = \dfrac{9-x^{2}}{x-3}$
NOT a Vertical Asymptote. Why?

According to Skeeter, x = 3 is a vertical asymptote.

Where did I say that?

I said $f(x) = \dfrac{5 - x^2}{x-3}$ had the vertical asymptote at $x=3$, not the function cited by tkhunny.

 

[mathdad]

Where did I say that?

I said $f(x) = \dfrac{5 - x^2}{x-3}$ had the vertical asymptote at $x=3$, not the function cited by tkhunny.

Sorry about the confusion.