Graph the square root functions f(x) = sqrt(x-2) and g(x) = sqrt(2-x). Which functi...

1. Understand y-intercept: A y-intercept is the point where a graph crosses the y-axis. This occurs when the x-coordinate is 0. To find the y-intercept of a function, we substitute $x=0$ into the function's equation.

2. Check function $f(x)$ for y-intercept: The function is $f(x) = \sqrt{x-2}$. Substitute $x=0$ into the function:
$$f(0) = \sqrt{0-2} = \sqrt{-2}$$Since the square root of a negative number is not a real number, $f(x)$ does not have a y-intercept in the real number system. The domain of $f(x)$ is $x \ge 2$.

3. Check function $g(x)$ for y-intercept: The function is $g(x) = \sqrt{2-x}$. Substitute $x=0$ into the function:
$$g(0) = \sqrt{2-0} = \sqrt{2}$$Since $\sqrt{2}$ is a real number, $g(x)$ has a y-intercept at $(0, \sqrt{2})$. The domain of $g(x)$ is $x \le 2$.

1. Compare results: Function $f(x)$ does not have a y-intercept, while function $g(x)$ does have a y-intercept.

1. Select the correct option: The question asks which function has a y-intercept. Based on the analysis, only $g(x)$ has a y-intercept. Therefore, the correct option is the one that includes $g(x)$.