Question

Create a rational function that meets the following criteria.Vertical Asymptotes at x = 5 and x = -3Hole in the graph at x = -1Horizontal Asymptote at y = 7Leave your answer in factored form (do not multiply the factors out)

Answer 1

`\begin{gathered} \text{ A vertical asymptote implies a denominator of a function where x=0 therefore} \\ x=5\rightarrow x-5=0\rightarrow(x-5) \\ x=-3\rightarrow x-3=0\rightarrow(x-3) \\ \text{ A hole in the graph at x=-1 implied that the factor is both on numerator and denominator} \\ \text{ Therefore,} \\ x=-1\rightarrow(x+1)\text{ is both on numerator and denominator} \\ \text{ A horizontal asymptote at y=7 means the numerator and denominator} \\ \text{ have their coefficients at 7:1} \\ \text{ Putting it together we have} \\ (7(x+1))/(1(x-5)(x-3)(x+1)) \\ \text{simplify and we get }(7(x+1))/((x-5)(x-3)(x+1)) \end{gathered}`