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.

(1 point)
Responses

f(x)
f of x

g(x)
g of x

both f(x) and g(x)
both f(x) and g(x)

Answer 1

To determine the y-intercepts of the functions \( f(x) = \sqrt{x - 2} \) and \( g(x) = \sqrt{2 - x} \), we evaluate each function at \( x = 0 \).

1. For \( f(x) = \sqrt{x - 2} \): \[ f(0) = \sqrt{0 - 2} = \sqrt{-2} \] This expression is undefined because the square root of a negative number is not real. Therefore, \( f(x) \) does not have a y-intercept.

2. For \( g(x) = \sqrt{2 - x} \): \[ g(0) = \sqrt{2 - 0} = \sqrt{2} \] This expression is defined and gives a real value, \( \sqrt{2} \). Therefore, \( g(x) \) has a y-intercept.

Since only \( g(x) \) has a y-intercept, the answer is:

g(x)