Graph the rational function. \[ f(x)=\frac{2 x+6}{-x-4} \] Start by drawing the vertical and horizontal asymptotes.

To begin graphing the rational function \( f(x)=\frac{2x+6}{-x-4} \), first identify the vertical asymptote by setting the denominator equal to zero: \(-x - 4 = 0\) leads to \(x = -4\). Next, for the horizontal asymptote, we look at the degrees of the polynomials in the numerator and denominator. Since both have a degree of 1, we take the ratio of the leading coefficients. The leading coefficient of the numerator (2) and the denominator (-1) gives us a horizontal asymptote at: \(y = \frac{2}{-1} = -2\). Now, plot the vertical asymptote at \(x = -4\) (a dashed line) and the horizontal asymptote at \(y = -2\) (another dashed line). To complete the graph, consider the behavior of the function around these asymptotes. For instance, as \(x\) approaches -4 from the left, \(f(x)\) will tend toward positive infinity, and as it approaches from the right, \(f(x)\) will head toward negative infinity. Additionally, for very large or very small values of \(x\), \(f(x)\) will approach -2, indicating how both the left and right portions of the graph behave. Finding additional points will make your graph more precise, and don't forget to indicate that the function cannot cross the vertical asymptote! Happy graphing!