Chapter 4.3, Problem 60AYU

Create a rational function that has the following characteristics: crosses the $x\text{-axis}$ at 2; touches the $x\text{-axis}$ at $-1$; one vertical asymptote at $x=-5$ and another at $x=6$; and one horizontal asymptote, $y=3$. Compare your function to a fellow classmate's. How do they differ? What are their similarities?

To determine

To find: How do they differ? What are their similarities?

Answer to Problem 60AYU

$y=\frac{3\left(x-2\right){\left(x+1\right)}^2}{\left(x+5\right){\left(x-6\right)}^2}$

Explanation of Solution

Given:

Create a rational function that has the following characteristics: crosses the $x\text{-axis}$ at 2; touches the $x\text{-axis}$ at $-1$; one vertical asymptote at $x=-5$ and another at $x=6$; and one horizontal asymptote, $y=3$. Compare your function to a fellow classmate’s.

crosses the $x\text{-axis}$ at 2; touches the $x\text{-axis}$ at $-1$;

one vertical asymptote at $x=-5$ and another at $x=6$; and

one horizontal asymptote, $y=3$.

That is the equation

$y=\frac{3\left(x-2\right){\left(x+1\right)}^2}{\left(x+5\right){\left(x-6\right)}^2}$