Graph the function. Plot all necessary asymptotes. For vertical asymptotes, make sure there are at least two points on each side. \( r(x)=\frac{-8}{2 x+3} \)

To graph the function \( r(x) = \frac{-8}{2x+3} \) and plot all necessary asymptotes, we need to identify the vertical asymptote(s) and the horizontal asymptote. 1. **Vertical Asymptote(s):** - The vertical asymptote(s) occur when the denominator of the function is equal to zero. - Set the denominator \(2x+3\) equal to zero and solve for \(x\): \[ 2x + 3 = 0 \] \[ 2x = -3 \] \[ x = -\frac{3}{2} \] - Therefore, the vertical asymptote is at \(x = -\frac{3}{2}\). 2. **Horizontal Asymptote:** - The horizontal asymptote is determined by the degree of the numerator and the denominator. - In this case, the degree of the numerator is 0 (constant term) and the degree of the denominator is 1 (linear term). - Since the degree of the numerator is less than the degree of the denominator, the horizontal asymptote is the x-axis, which is \(y = 0\). Now, let's plot the function and the asymptotes on a graph.