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: both f(x)
and g(x)
(1 point)
Option

Answer 1

To determine which function has a y-intercept, we can evaluate both functions at \( x = 0 \).

**For the function \( f(x) = \sqrt{x - 2} \):**
- \( f(0) = \sqrt{0 - 2} = \sqrt{-2} \), which is not defined (the square root of a negative number).

**For the function \( g(x) = \sqrt{2 - x} \):**
- \( g(0) = \sqrt{2 - 0} = \sqrt{2} \), which is defined and is a real number.

Since \( f(x) \) does not have a y-intercept (it is not defined at \( x = 0 \)), while \( g(x) \) does, the correct answer is:

**Option 2: g(x)**