Use the image to answer the question.

Question

A coordinate plane's axes range from negative 5 to 5 by 1-unit increments. Two rays are plotted. The first ray starts from a closed endpoint, while the second ray starts from an open endpoint.

Determine which equations are the piecewise linear functions on the graphs.

Option #1: f(x)={−2x−1, x≤2−x+4, x>2

Option #2: f(x)={2x−1, x≥2x+4, x<2

(1 point)
Option #
is the correct piecewise function.

Answer 1

To determine which option represents the piecewise linear function based on the description of the rays, we would need to analyze the endpoints and slopes given in the options.

1. Option #1:

   • \( f(x) = -2x - 1 \) for \( x \leq 2 \)
   • \( f(x) = -x + 4 \) for \( x > 2 \)

2. Option #2:

   • \( f(x) = 2x - 1 \) for \( x \geq 2 \)
   • \( f(x) = x + 4 \) for \( x < 2 \)

Given that one ray starts from a closed endpoint and the other from an open endpoint, we can conclude:

• A closed endpoint would suggest that the function is defined at that particular point, which typically aligns with the \( \leq \) or \( \geq \) condition.
• An open endpoint means the function does not include that specific point, aligning with the \( < \) or \( > \) condition.

Since you mentioned one ray starts from a closed endpoint (which could correspond to one half of the piecewise function), we can infer that Option #1 has the correct structure with \( x \leq 2 \) having a closed endpoint and \( x > 2 \) having an open endpoint.

Therefore, Option #1 represents the correct piecewise function based on your description.