Question: Graph the function below. Use the given points to plot the horizontal asymptote, vertical…

Graph the function below. Use the given points to plot the horizontal asymptote, vertical asymptote, and x-intercept:

\[ y = \frac{35}{(x - 2)} - 5 \]

Solution

Step 1: Identify the vertical asymptote. \[ x - 2 = 0 & \] Vertical asymptote at \( x = 2 \). Step 2: Identify the horizontal asymptote. As \( x \) approaches infinity, \( \frac{35}{x - 2} \) approaches 0. \[ y = -5 & \] Horizontal asymptote at \( y = -5 \). Step 3: Find the x-intercept by setting \( y = 0 \). \[ 0 = \frac{35}{x - 2} - 5 & \] \[ \frac{35}{x - 2} = 5 & \] \[ 35 = 5(x - 2) & \] \[ 35 = 5x - 10 & \] \[ 5x = 45 & \] \[ x = 9 & \] X-intercept at \( x = 9 \).