Question

If a function is undefined, does it have a horizontal asymptote?

Answer 1

If a function is undefined at some value of x, then there is a vertical asymptote at that value of x. Alternatively, you could have a step function which is undefined at some value of x.

Answer 2

@RBauer4 , so then if you have f(x) which is undefined at some value of y, you will have a horizontal aymptote?

Answer 3

actually the y value is undefined i mean. the limit of a function that i calculated is undefined and is asking if there is a horizontal asymptote or not

Answer 4

Is it a function of y or a function of x? That's is f(y) or f(x)?

Answer 5

\[\lim_{x \infty \rightarrow ?}\frac{ x^5(40+\frac{ 1 }{ x^3 } }{ x^5(\frac{ 16 }{ x }-\frac{ 2 }{ x^4 }) }=\frac{ 40+0 }{ 0-0 }=undefined\]

Answer 6

then after they are asking if there is a horizontal aymptote.

Answer 7

*lim x-->infinity

Answer 8

No, there is not a horizontal asymptote and you calculated your limit correctly. If you think about it, since the degree of the numerator is greater than the degree of the denominator, the function value of f(x) will get larger and larger as x gets larger. There is a sort of trick when dealing with rational functions that involves three cases. When the degree of the numerator is greater than that of the denominator, the function will diverge towards infinity.

Answer 9

diverge towards infinity means? subdivide to infinity? isnt that an asymptote? haha omg im so confused

Answer 10

I'm sorry to confuse you. What I mean is that the function will approach infinity as x approaches infinity. Imagine a function like this

A function like this appears to approach infinity as x becomes very large. In other words, as x becomes huge, so does y.