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

In summary, the vertical asymptote of the function f(x) = (5 - x^2)/(x - 3) is x = 3. This is because at x = 3, the denominator of the function becomes undefined, causing a discontinuity in the function. The function g(x) = (9 - x^2)/(x - 3) is also not a vertical asymptote, as it has a non-zero value at x = 3. The words discontinuity and vertical asymptote are related, as a vertical asymptote is a type of discontinuity in a function.
  • #1
mathdad
1,283
1
Find the vertical asymptote of f(x) = (5 - x^2)/(x - 3). I need the steps not the solution.
 
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  • #2
Vertical asymptote is x = 3 ... why?
 
  • #3
RTCNTC said:
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?
 
  • #4
skeeter said:
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?
 
  • #5
tkhunny said:
$g(x) = \dfrac{9-x^{2}}{x-3}$

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?
 
  • #6
RTCNTC said:
tkhunny said:
$g(x) = \dfrac{9-x^{2}}{x-3}$
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.
 
  • #7
skeeter said:
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.
 

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

What is a vertical asymptote?

A vertical asymptote is a vertical line on a graph that represents a value or point where the function becomes undefined or approaches infinity.

How do you find the vertical asymptote of a function?

To find the vertical asymptote of a function, you must set the denominator of the function equal to zero and solve for the variable. The resulting value is the x-coordinate of the vertical asymptote.

Can a vertical asymptote intersect with the graph of a function?

No, a vertical asymptote cannot intersect with the graph of a function because the function becomes undefined at that point and the graph cannot be drawn.

What is the difference between a vertical asymptote and a horizontal asymptote?

A vertical asymptote represents a value where the function becomes undefined, while a horizontal asymptote represents a value that the function approaches as x approaches infinity or negative infinity.

Can a function have more than one vertical asymptote?

Yes, a function can have multiple vertical asymptotes if the denominator of the function has more than one value that makes it equal to zero.

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