To determine which, if any, of the functions \( f(x) = \sqrt{x} - 2 \) or \( g(x) = \sqrt{x} - 2 \) has a y-intercept, we need to evaluate each function at \( x = 0 \).
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Calculating the y-intercept for \( f(x) \): \[ f(0) = \sqrt{0} - 2 = 0 - 2 = -2 \] So, the y-intercept of \( f(x) \) is \( (0, -2) \).
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Calculating the y-intercept for \( g(x) \): Since \( g(x) \) is identical to \( f(x) \) (i.e., \( g(x) = \sqrt{x} - 2 \)), the calculation is the same: \[ g(0) = \sqrt{0} - 2 = 0 - 2 = -2 \] Thus, the y-intercept of \( g(x) \) is also \( (0, -2) \).
Since both functions \( f(x) \) and \( g(x) \) yield a y-intercept at \( (0, -2) \), the correct response is:
both f(x) and g(x)