Find the \( x \)-intercept(s) and \( y \)-intercept(s) of the graph of the following. \[ y=\frac{-9 x+5}{x^{2}+9} \] If there is more than one answer, separate them with commas. Click on "None" if applicable. \( x \)-intercept(s):

To find the \( x \)-intercept(s) of the graph of the function \( y = \frac{-9x + 5}{x^2 + 9} \), we set \( y = 0 \) and solve for \( x \). The equation becomes: \[ 0 = \frac{-9x + 5}{x^2 + 9} \] For the fraction to equal zero, the numerator must be zero (as long as the denominator is not zero). Therefore, we set the numerator equal to zero: \[ -9x + 5 = 0 \] Solving for \( x \): \[ -9x = -5 \\ x = \frac{5}{9} \] Thus, the \( x \)-intercept is: \[ \left( \frac{5}{9}, 0 \right) \] Next, we find the \( y \)-intercept(s) by setting \( x = 0 \) in the function: \[ y = \frac{-9(0) + 5}{0^2 + 9} = \frac{5}{9} \] Thus, the \( y \)-intercept is: \[ (0, \frac{5}{9}) \] In summary, the intercepts are: - \( x \)-intercept(s): \( \frac{5}{9} \) - \( y \)-intercept(s): \( \frac{5}{9} \) So, the final answers are: - \( x \)-intercept(s): \( \frac{5}{9} \) - \( y \)-intercept(s): \( \frac{5}{9} \)