Question

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)

Answer 1

To determine which function has a y-intercept, we need to find the value of each function when \( x = 0 \).

1. **For \( f(x) = \sqrt{x - 2} \)**:
- Substitute \( x = 0 \):
\[
f(0) = \sqrt{0 - 2} = \sqrt{-2}
\]
Since the square root of a negative number is not real, \( f(0) \) is not defined. Thus, \( f(x) \) has no y-intercept.

2. **For \( g(x) = \sqrt{2 - x} \)**:
- Substitute \( x = 0 \):
\[
g(0) = \sqrt{2 - 0} = \sqrt{2}
\]
This is a real number, so \( g(x) \) has a y-intercept.

From the analysis above, only \( g(x) \) has a y-intercept.

The correct option is:
**Option 2: g(x)**.