Question

Graph the square root functions f(x)=√x − 2 and g(x)=√2 − x. Which function has a y-intercept?
f(x)
g(x)
neither f(x) or g(x)
both f(x) and g(x)

Answer 1

To determine which function has a y-intercept, let's analyze the functions \( f(x) = \sqrt{x} - 2 \) and \( g(x) = \sqrt{2 - x} \).

1. **Finding the y-intercept**:
The y-intercept occurs when \( x = 0 \).

- For \( f(x) = \sqrt{x} - 2 \):
\[
f(0) = \sqrt{0} - 2 = 0 - 2 = -2
\]
So, the y-intercept of \( f(x) \) is \((0, -2)\).

- For \( g(x) = \sqrt{2 - x} \):
\[
g(0) = \sqrt{2 - 0} = \sqrt{2}
\]
So, the y-intercept of \( g(x) \) is \((0, \sqrt{2})\).

2. **Conclusion**:
Both functions \( f(x) \) and \( g(x) \) have y-intercepts.

Thus, the answer is: **both \( f(x) \) and \( g(x) \)**.