To determine which function has a y-intercept, we first need to analyze both functions.
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Function \( f(x) = \sqrt{x - 2} \):
- The function is defined when \( x - 2 \geq 0 \), which means \( x \geq 2 \).
- Thus, \( f(x) \) does not have a y-intercept because it is not defined for \( x = 0 \) or any value less than 2.
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Function \( g(x) = \sqrt{2 - x} \):
- The function is defined when \( 2 - x \geq 0 \), which means \( x \leq 2 \).
- To find the y-intercept, we set \( x = 0 \): \[ g(0) = \sqrt{2 - 0} = \sqrt{2} \]
- The y-intercept of \( g(x) \) is \( \sqrt{2} \).
Based on the analysis:
- The function \( g(x) \) has a y-intercept, while \( f(x) \) does not.
Therefore, the correct response is:
- g(x)