Using the asymptote concept, the function with a vertical asymptote at x = 3 and an horizontal asymptote at is given by:
- The vertical asymptotes are the values of x which are outside the domain, which in a fraction are the zeroes of the denominator.
- The horizontal asymptote is the value of f(x) as x goes to infinity, as long as this value is different of infinity.
The vertical asymptote at x = 3 means that x = 3 is a root of the denominator, hence:
The horizontal asymptote at y = -1/2 means that:
Which happens if , hence the function is:
More can be learned about asymptotes at brainly.com/question/16948935
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