I've been told that "It's okay for the numerator to be 0. It's not okay for the denominator to be 0 because then the number would be undefined," however, to find the vertical asymptote, you have to make the demoniator 0! So how is this correct?
if you have x+1/x+2, X has to equal -2, so the vertical line can also be -2! This is how I've been doing it.
So the problem i asked earlier: -3x/x+2... why can't x = -2?!? There's a VA of -2 ( i put it in the calculator) so why say no?
Thanks.
if you have x+1/x+2, X has to equal -2, so the vertical line can also be -2! This is how I've been doing it.
So the problem i asked earlier: -3x/x+2... why can't x = -2?!? There's a VA of -2 ( i put it in the calculator) so why say no?
Thanks.
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The denominator cannot equal 0, which is why the vertical asymptote is created.
Yes, you set the denominator equal to 0 and solve for x to find the asymptote, but remember what an asymptote is. An asymptote does not represent solutions to the equation. On the contrary, it represents values the function approaches, but never reaches.
Yes, you set the denominator equal to 0 and solve for x to find the asymptote, but remember what an asymptote is. An asymptote does not represent solutions to the equation. On the contrary, it represents values the function approaches, but never reaches.
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You might be getting 'wrong' answers because you wrote the problem wrong.
It looks like you meant -3x/(x+2). Remember your order of operations. Division comes before addition. If you want x+2 to be the denominator then you need parentheses around it.
(note: you don't need the parentheses on paper because the horizontal line tells you what's in the denominator)
y = -3x/(x+2) has the vertical asymptote x = -2
y = -3x/x+2 has no asymptote.
Also, There's more to finding vertical asymptotes than just finding where division by zero occurs. A division by zero only tells you that there's a potential asymptote there. It isn't always one. Once you figure out what makes the denominator zero you need to use some other method to determine if there's an asymptote there.
In general this means finding the limit. If x =c gives you a division by zero then find the limit as x approaches c of f(x). If either the left or right limit is ±infinity then there's a vertical asymptote. In fact, that's pretty much the definition of a vertical asymptote.
Finding the limit will always work but there are shortcuts that you can use for rational functions. If the numerator is not zero when x = c but the denominator is zero, then x = c is a vertical asymptote.
You can also try factoring the numerator and denominator. Then cancel common factors. If what remains still gives you division by zero (and a nonzero numerator) then you have a vertical asymptote. If the factors cancel so that you no longer have division by zero then you have a removable discontinuity.
y = -3x/x+2 is a good example of a function that has a division by zero but does NOT have a vertical asymptote. This is because the x's cancel out. You have a removable discontinuity (a hole) instead of an asymptote.
It looks like you meant -3x/(x+2). Remember your order of operations. Division comes before addition. If you want x+2 to be the denominator then you need parentheses around it.
(note: you don't need the parentheses on paper because the horizontal line tells you what's in the denominator)
y = -3x/(x+2) has the vertical asymptote x = -2
y = -3x/x+2 has no asymptote.
Also, There's more to finding vertical asymptotes than just finding where division by zero occurs. A division by zero only tells you that there's a potential asymptote there. It isn't always one. Once you figure out what makes the denominator zero you need to use some other method to determine if there's an asymptote there.
In general this means finding the limit. If x =c gives you a division by zero then find the limit as x approaches c of f(x). If either the left or right limit is ±infinity then there's a vertical asymptote. In fact, that's pretty much the definition of a vertical asymptote.
Finding the limit will always work but there are shortcuts that you can use for rational functions. If the numerator is not zero when x = c but the denominator is zero, then x = c is a vertical asymptote.
You can also try factoring the numerator and denominator. Then cancel common factors. If what remains still gives you division by zero (and a nonzero numerator) then you have a vertical asymptote. If the factors cancel so that you no longer have division by zero then you have a removable discontinuity.
y = -3x/x+2 is a good example of a function that has a division by zero but does NOT have a vertical asymptote. This is because the x's cancel out. You have a removable discontinuity (a hole) instead of an asymptote.