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  • State a possible rational function that satisfies the following conditions:   it has these asymptotes x=-3x=+2 y=3

    • and 

  • it intersects the x axis at 1 and 3The presence of the vertical asymptotes x=−3 and x=2 implies that the denominator also contains factors (x+3) and (x−2).

  • It follows that the horizontal asymptote y=3 indicates that upon simplification, dividing the leading coefficients of both the numerator and denominator must yield 3.

  • From graph, it is clear that the x-intercepts are situated at x=1 and x=3. This implies that the numerator must comprise factors (x−1) and (x−3).Explain by showing all steps how your rational functions satisfies the conditions above.   

    • The vertical asymptotes at x=−3 and x=2 can be attributed to the denominator equations which included the factors (x+3) and (x−2) respectively. Thus the function is undefined at these values leading to the vertical asymptotes.The horizontal line at y=3 is known because the degrees of both the numerator and denominator are equal; 3 is in the numerator and 1 in the denominator leading to a horizontal asymptote of y=3.Function therefore has x-intercepts at x=1 and x=3 where function becomes zeros as the numerator contains (x−1) and (x−3) respectively.

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