Graph the rational function.

Start by drawing the vertical and horizontal asymptotes.

To graph the function , begin by identifying the vertical and horizontal asymptotes. The vertical asymptote occurs when the denominator is zero, so set . Solving this gives . For the horizontal asymptote, since the degree of the numerator (0) is less than the degree of the denominator (1), the horizontal asymptote is .

Now you can sketch the graph: plot the vertical line at and the horizontal line at . The function will approach these lines but never touch them. These asymptotes are essential for understanding the behavior of the graph as approaches these critical values.

Lastly, plug in a few values of to get points on the graph, noting that as approaches -1 from the left, will trend towards , and as it approaches from the right, it will trend towards . To the left of , the values of will be negative, and to the right, they will be positive. Happy graphing!