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

Respuesta :

LearnGrow
x=3 is a vertical line . The question is "Is this line a vertical asymptotefor the function f(x)?". Vertical asymptote is vertical line near which the function grows without bound.
The function f(x)=5x-15/x-3 is not asymptotic to the line x=3, because for x=3 f(x)=5*3-15/3-3=0/0=0 . So, there is a value for x=3 and the function f(x) does not grow near x=3 without bound.

facundo3141592

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:

[tex]f(x) = \frac{5x - 15}{x - 3}[/tex]

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:

[tex]f(x) = \frac{5*x - 15}{x - 3} = \frac{5*(x - 3)}{(x - 3)} = 5[/tex]

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:

https://brainly.com/question/4084552

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