Question

Question
Use the image to answer the 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 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={−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={−2x3x
y equals left brace line 1 negative 2 time x line 2 3 times x
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Answer 1

To identify the correct piecewise function based on the description of the rays on the coordinate plane:

1. One ray has an **open** endpoint and is represented with \( y = -2 \) for some values of \( x \).
2. The other ray has a **closed** endpoint and is represented with \( y = 3 \) for some values of \( x \).

From the given options, here’s a breakdown:

- **Option 1:** \( y = \{ -2, x < 0 \\ 3, x \geq 0 \} \)
This suggests the ray starting at the open endpoint (y = -2) is valid for \( x < 0 \), and the closed endpoint (y = 3) starts at \( x = 0 \) and goes right. This is a possible representation of the rays.

- **Option 2:** \( y = \{ -2, x < 2 \\ 3, x \leq 3 \} \)
This suggests the rays would continue up to \( x = 2 \) but does not appropriately fit the described behavior of the open and closed endpoints.

- **Option 3:** \( y = \{ -2, x > 0 \\ 3, x < 0 \} \)
This has the open ray starting at \( x = 0 \), which contradicts the description since it should be closed for \( y = 3 \) starting at \( x = 0\).

- **Option 4:** \( y = \{ -2x \\ 3x \} \)
This option does not represent horizontal rays but linear equations instead.

The most fitting description provided is **Option 1:**

**Response:** \( y = \{ -2, x < 0 \\ 3, x \geq 0 \} \)