Given that \( g(x)=\frac{x-6}{x+5} \), find each of the following. \( \begin{array}{lllll}\text { a) } g(9) & \text { b) } g(6) & \text { c) } g(-5) & \text { d) } g(-13.25) & \text { e) } g(x+h)\end{array} \)

Let's calculate each of the values for the function \( g(x) = \frac{x-6}{x+5} \): **a) \( g(9) \)** \[ g(9) = \frac{9 - 6}{9 + 5} = \frac{3}{14} \] **b) \( g(6) \)** \[ g(6) = \frac{6 - 6}{6 + 5} = \frac{0}{11} = 0 \] **c) \( g(-5) \)** Here, the function \( g(x) \) is undefined because the denominator becomes zero. \[ g(-5) = \frac{-5 - 6}{-5 + 5} = \text{undefined} \] **d) \( g(-13.25) \)** \[ g(-13.25) = \frac{-13.25 - 6}{-13.25 + 5} = \frac{-19.25}{-8.25} = \frac{19.25}{8.25} = \frac{77}{33} \quad \text{(approximately 2.33)} \] **e) \( g(x+h) \)** To find \( g(x+h) \): \[ g(x+h) = \frac{(x+h) - 6}{(x+h) + 5} = \frac{x + h - 6}{x + h + 5} = \frac{x + h - 6}{x + h + 5} \] So, to summarize, we have: - \( g(9) = \frac{3}{14} \) - \( g(6) = 0 \) - \( g(-5) = \text{undefined} \) - \( g(-13.25) = \frac{77}{33} \) - \( g(x+h) = \frac{x + h - 6}{x + h + 5} \)