Graph the square root functions f(x)=x−2−−−−√

Question

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 need to evaluate both functions at \( x = 0 \) and see if they yield a valid output.

1. For the first function, \( f(x) = \sqrt{x - 2} \):

   • When \( x = 0 \): \[ f(0) = \sqrt{0 - 2} = \sqrt{-2} \] This is not a real number, so there is no y-intercept for \( f(x) \).

2. For the second function, \( g(x) = \sqrt{2 - x} \):

   • When \( x = 0 \): \[ g(0) = \sqrt{2 - 0} = \sqrt{2} \] This is a valid real number, so there is a y-intercept at \( y = \sqrt{2} \).

Therefore, the answer is:

Option 2: g(x)