Explain why the function f(x)= 5x-15/x-3 is not asymptotic to the line x=3. sketch the graph of this function.

We define an asymptote as a tendency to a given value, such that the value is never reached. We usually have vertical asymptotes in situations where the denominator of a function becomes zero.

We will see that we do not have an asymptote at x = 3 because the denominator can be simplified and the function is actually a constant.

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Let's see how to get the answer.

Here we start with the function:

And we want to see why this function does not have an asymptote at x = 3 (where the denominator is equal to zero).

This can happen because the denominator can be simplified.

If we write the numerator as:

5*x - 15 = 5*(x - 3)

Then we get:

So the numerator also became 0 when the denominator was zero, that is why we didn't have an asymptote at x = 3.

If you want to learn more, you can read:

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