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

y={−2, x>23, x≤3

Answer 1

To determine the correct piecewise function corresponding to the two rays on the coordinate plane, we need to analyze the characteristics of each ray based on the descriptions you've provided.

1. The first ray has an open endpoint, which means it does not include that endpoint in its function definition. This suggests that the function might involve the constraint \( x > 0 \) for that part of the piecewise function.

2. The second ray starts from a closed endpoint, indicating that this part is included in the function. Therefore, it would use \( x \geq 0 \) for its definition.

Based on this analysis, the piecewise function must define the following:

• For the ray starting from the open endpoint (let’s say it is represented by a constant value \(-2\)), it applies when \( x > 0 \).
• For the ray with the closed endpoint (assuming it’s represented by a constant value \(3\)), it applies when \( x \leq 0 \).

So we can write the piecewise function as:

\[ y = \begin{cases} -2, & x > 0 \ 3, & x \leq 0 \end{cases} \]

Looking at the options provided in your question, we can see that the correct piecewise function matching our conclusion is:

y={−2, x>0 \ 3, x≤0}

Final answer: y={−2, x>0 \ 3, x≤0}