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)

Answer 1

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

1. For \( f(x) = \sqrt{x - 2} \):
- \( f(0) = \sqrt{0 - 2} = \sqrt{-2} \) (This is not a real number. Therefore, \( f(x) \) does not have a y-intercept in the real number system.)

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

Based on this evaluation:

- **Option 1: f(x)** does not have a y-intercept.
- **Option 2: g(x)** does have a y-intercept.
- **Option 3: both f(x) and g(x)** is incorrect since only \( g(x) \) has a y-intercept.

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