To determine which function has a y-intercept, we need to evaluate each function at \( x = 0 \).
1. For \( f(x) = \sqrt{x - 2} \):
- The y-intercept occurs when \( x = 0 \): \[ f(0) = \sqrt{0 - 2} = \sqrt{-2} \] Since \(\sqrt{-2}\) is not a real number, \( f(x) \) does not have a y-intercept.
2. For \( g(x) = \sqrt{2 - x} \):
- The y-intercept occurs when \( x = 0 \): \[ g(0) = \sqrt{2 - 0} = \sqrt{2} \] This is a real number, so \( g(x) \) has a y-intercept.
Conclusion:
- Only \( g(x) \) has a y-intercept.
The correct option is:
Option 2: \( g(x) \)