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={−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<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>23, x≤3
y equals left brace line 1 negative 2 comma x less than 2 line 2 3 comma x less than or equal to 3

y={−2x3x

Answer 1

Based on the description provided, we can analyze the possible piecewise functions.

1. The first ray starts from an open endpoint, which typically indicates that its corresponding value at that point is not included in the function (this often is represented with ">" or "<").
2. The second ray starts from a closed endpoint, which suggests that its value at that point is included in the function (represented with "≥" or "≤").

Given this structure, the correct choice would involve:

• A value of -2 for certain x values (possibly for x < certain threshold) which represents the first ray (open endpoint).
• A value of 3 for x values above or equal to a threshold indicating the second ray (closed endpoint).

Thus, the correct piecewise function should represent:

• An open endpoint at x = 0 for y = -2, which corresponds to \( y = -2 \) when \( x > 0 \).
• A closed endpoint at x = 0 for y = 3 representing \( y = 3 \) when \( x \leq 0 \).

The most suitable option among the ones provided is:

y={−2, x>0; 3, x≤0

This represents the behavior described for both rays appropriately.