Question

Graph the square root functions and .

Which function has a y-intercept?

(1 point)
Responses

f(x)
f of x

g(x)
g of x

both f(x) and g(x)

Answer 1

To respond to your question about the square root functions \( f(x) \) and \( g(x) \), I will assume you're referring to two functions of the form \( f(x) = \sqrt{x} \) and \( g(x) = \sqrt{x - c} \) for some constant \( c \).

Let’s outline the characteristics of these functions:

1. **Function \( f(x) = \sqrt{x} \):**
- This function starts at the origin (0,0) and only exists for \( x \geq 0 \).
- Its y-intercept is at \( (0, 0) \), since when \( x = 0 \), \( f(0) = \sqrt{0} = 0 \).

2. **Function \( g(x) = \sqrt{x - c} \):**
- This function will have a y-intercept only if \( c \leq 0 \) because \( g(0) = \sqrt{0 - c} \) must be defined (i.e., non-negative).
- If \( c > 0 \), \( g(x) \) does not have a y-intercept because \( g(0) \) would attempt to take the square root of a negative number, which is undefined in the realm of real numbers.

### Determining which function has a y-intercept:
- **If** \( c \) is chosen such that \( c \leq 0 \), then **both** functions will have a y-intercept.
- **If** \( c > 0 \), then only \( f(x) \) has a y-intercept.

### Answer:
- If \( g(x) \) has a y-intercept (meaning \( c \leq 0 \)), the answer would be “both \( f(x) \) and \( g(x) \).”
- If \( c > 0\), the answer would be “\( f(x) \).”

Please clarify or provide specific forms of the functions you're referring to for more precise guidance!