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

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

f(x)
f of x

g(x)
g of x

Answer 1

To determine which function has a y-intercept, we first need to analyze both functions.

1. Function \( f(x) = \sqrt{x - 2} \):

   • The function is defined when \( x - 2 \geq 0 \), which means \( x \geq 2 \).
   • Thus, \( f(x) \) does not have a y-intercept because it is not defined for \( x = 0 \) or any value less than 2.

2. Function \( g(x) = \sqrt{2 - x} \):

   • The function is defined when \( 2 - x \geq 0 \), which means \( x \leq 2 \).
   • To find the y-intercept, we set \( x = 0 \): \[ g(0) = \sqrt{2 - 0} = \sqrt{2} \]
   • The y-intercept of \( g(x) \) is \( \sqrt{2} \).

Based on the analysis:

• The function \( g(x) \) has a y-intercept, while \( f(x) \) does not.

Therefore, the correct response is:

• g(x)