Use the image to answer the question.

Question

A coordinate plane's axes range from negative 10 to 10 by 1-unit increments. Two rays are plotted. The first ray starts from an open endpoint, while the second ray starts from a closed endpoint.

Choose the correct piecewise function.

(1 point)
Responses

y={−2x3x
y equals left brace line 1 negative 2 time x line 2 3 times x

y={−2, x<03, x≥0
y equals left brace line 1 negative 2 comma x less than zero line 2 3 comma x less than or equal to zero

y={−2, x>03, x>0
y equals left brace line 1 negative 2 comma x greater than 0 line 2 3 comma x less than 0

y={−2, x>23, x≤3

Answer 1

To determine the correct piecewise function based on the description of the rays, we need to interpret the conditions of the endpoints:

1. The first ray (starting from an open endpoint) would indicate that the function is not defined at that point but exists beyond that point.
2. The second ray (starting from a closed endpoint) indicates that the function includes the value at that specific point.

Based on the responses provided, "y={−2, x<03, x≥0" suggests that y = -2 for x < 0 and y = 3 for x ≥ 0. This would correspond to a ray that starts from the open side at x = 0 (not including the value of -2 for that x) and then takes on the value 3 at and beyond that point (which is a closed side).

The other options do not conform to the description of one ray beginning at an open endpoint and the other beginning at a closed endpoint.

Therefore, the correct piecewise function based on the provided conditions should be:

y={−2, x<0; 3, x≥0