What are the \( x \)-intercepts of the given rational function below? \( f(x)=\frac{x-4}{x^{2}+2 x-48} \) \( (5,0) \) and \( (1,0) \) \( (4,0) \) \( (0,0) \) \( (1,0) \)

To find the \( x \)-intercepts of the rational function \( f(x) = \frac{x - 4}{x^{2} + 2x - 48} \), we need to determine the values of \( x \) that make \( f(x) = 0 \). ### Steps to Find the \( x \)-Intercepts: 1. **Set the numerator equal to zero:** \[ x - 4 = 0 \implies x = 4 \] 2. **Ensure the denominator is not zero at \( x = 4 \):** \[ x^2 + 2x - 48 = (4)^2 + 2(4) - 48 = 16 + 8 - 48 = -24 \neq 0 \] Since the denominator is not zero when \( x = 4 \), this is a valid \( x \)-intercept. 3. **Conclusion:** The function has a single \( x \)-intercept at \( (4, 0) \). ### Answer: \( (4,\ 0) \)