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 with closed endpoints and one line segment with two open endpoints are plotted.

Select the equation of the piecewise function shown in the graph.

(1 point)
Responses

y=⎧⎩⎨⎪⎪x+2, x≤−1x+3, −1<x<1x+1, x≥1
y equals left brace line 1 x plus 2, x is less than or equal to negative 1 line 2 x plus 3 comma negative 1 less than x less than 1 line 3 x plus 1 comma x greater than or equal to 1

y=⎧⎩⎨⎪⎪x+2, x<−1x+3, −1≤x≤1x+1, x>1
y equals left brace line 1 x plus 2, x is less than negative 1 line 2 x plus 3 comma negative 1 less than or equal to x less than or equal to 1 line 3 x plus 1 comma x greater than 1

y=⎧⎩⎨⎪⎪x+2, x≤1x+3, 2<x<4x+1, x≥2
y equals left brace line 1 x plus 2, x is less than or equal to negative 1 line 2 x plus 3 comma 2 less than x less than 4 line 3 x plus 1 comma x greater than or equal to 2

y=⎧⎩⎨⎪⎪x+1, x≤−1x+2, −1<x<1x+3, x≥1

Answer 1

Without the image, I am unable to determine the slopes and endpoints of the rays and line segments.

However, to choose the correct option from the provided equations, you would need to analyze the slopes and intercepts of the lines represented in each piece of the piecewise function according to the ranges given for \( x \).

Here’s how you can determine which piecewise function is correct based on typical characteristics:

1. Identify the slopes and y-intercepts for each segment of the piecewise function.
2. Check where the segments open and close. Closed endpoints typically indicate that the inequality includes the endpoint (≤ or ≥), while open endpoints do not (<>).
3. Match the function’s expression and the defined intervals against the graph for all specified portions.

Once you do this analysis by checking the conditions for each segment represented in the graph, the right equation will become evident. If you provide a detailed description of the graph and how the lines behave, I can assist in deriving the correct answer.