Question

Graph the square root functions f(x)=x−2−−−−√
and g(x)=2−x−−−−√
. Which function has a y
-intercept? Enter the correct option number.

Option 1: f(x)

Option 2: g(x)

Option 3: bothf(x)
and g(x)

(1 point)
Option

Answer 1

To determine which function has a y-intercept, we need to evaluate each function at \(x=0\):

1. For \(f(x) = \sqrt{x - 2}\):
- \(f(0) = \sqrt{0 - 2} = \sqrt{-2}\), which is not a real number. Thus, \(f(x)\) has no y-intercept.

2. For \(g(x) = \sqrt{2 - x}\):
- \(g(0) = \sqrt{2 - 0} = \sqrt{2}\), which is a real number. Hence, \(g(x)\) has a y-intercept.

Based on this evaluation, the answer is:

**Option 2: g(x)**