Question

Graph the square root functions f(x)=√x-2 and g(x)=√x-2. Which function has a y-intercept?
Responses

f(x)

g(x)

both f(x) and g(x)

neither function

Answer 1

To determine which, if any, of the functions \( f(x) = \sqrt{x} - 2 \) or \( g(x) = \sqrt{x} - 2 \) has a y-intercept, we need to evaluate each function at \( x = 0 \).

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

2. **Calculating the y-intercept for \( g(x) \)**:
Since \( g(x) \) is identical to \( f(x) \) (i.e., \( g(x) = \sqrt{x} - 2 \)), the calculation is the same:
\[
g(0) = \sqrt{0} - 2 = 0 - 2 = -2
\]
Thus, the y-intercept of \( g(x) \) is also \( (0, -2) \).

Since both functions \( f(x) \) and \( g(x) \) yield a y-intercept at \( (0, -2) \), the correct response is:

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