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)

Answer 1

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

**1. For \( f(x) = \sqrt{x - 2} \):**
- 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: \( g(x) \)**