A rational function \(r\) such that \(r\) has a vertical asymptote at \(x = -2\text{,}\) a zero at \(x = 1\text{,}\) a hole at \(x = 5\text{,}\) and a horizontal asymptote of \(y = -3\text{.}\)

A rational function \(u\) whose numerator has degree \(3\text{,}\) denominator has degree \(3\text{,}\) and that has exactly one vertical asymptote at \(x = -4\) and a horizontal asymptote of \(y = \frac{3}{7}\text{.}\)

A rational function \(w\) whose formula generates a graph with all of the characteristics shown in the following figure. Assume that \(w(5) = 0\) but \(w(x) \gt 0\) for all other \(x\) such that \(x \gt 3\text{.}\)

A rational function \(z\) whose formula satisfies the sign chart shown in the following figure, and for which \(z\) has no horizontal asymptote and its only vertical asymptotes occur at the middle two values of \(x\) noted on the sign chart.

A rational function \(f\) that has exactly two holes, two vertical asymptotes, two zeros, and a horizontal asymptote.