Find all \( x \)-intercepts of the following function. Write your answer or answers as coordinate points. Be sure to select the appropriate number of \( x \)-intercepts. \[ f(x)=\frac{2 x-16}{3 x^{2}+28 x+9} \]

To find the \( x \)-intercepts of the function \( f(x) = \frac{2x - 16}{3x^2 + 28x + 9} \), we need to determine where the function equals zero. The \( x \)-intercepts occur when the numerator is equal to zero, as long as the denominator is not also zero at those points. 1. **Set the numerator equal to zero:** \[ 2x - 16 = 0 \] 2. **Solve for \( x \):** \[ 2x = 16 \\ x = 8 \] Now we have one potential \( x \)-intercept at \( x = 8 \). 3. **Check the denominator to ensure it is not zero at \( x = 8 \):** \[ 3(8)^2 + 28(8) + 9 \] Calculating this: \[ 3(64) + 224 + 9 = 192 + 224 + 9 = 425 \] Since the denominator is not zero, \( x = 8 \) is indeed an \( x \)-intercept. 4. **Write the \( x \)-intercept as a coordinate point:** The \( x \)-intercept is \( (8, 0) \). Thus, the only \( x \)-intercept of the function is: \[ \boxed{(8, 0)} \]