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

y=⎧⎩⎨⎪⎪x+2, x≤1x+3, 2<x<4x+1, x≥2

A B C or D

Answer 1

To determine the correct piecewise function, we need to analyze the graph based on the descriptions of the lines and any endpoints specified.

From your descriptions:

• The first part \( x + 2 \) needs to apply to values less than some threshold, likely around or less than -1.
• The second part \( x + 3 \) appears to apply between -1 and 1, possibly including -1.
• The third part \( x + 1 \) seems to apply for \( x > 1 \), only including points greater than 1.

Based on these observations, the function will look something like:

• For \( x < -1 \), \( y = x + 2 \)
• For \( -1 \leq x \leq 1 \), \( y = x + 3 \)
• For \( x > 1 \), \( y = x + 1 \)

Comparing this interpretation with the provided responses, the correct piecewise function matches with option A:

\[ y = \begin{cases} x + 2 & \text{for } x < -1 \ x + 3 & \text{for } -1 \leq x \leq 1 \ x + 1 & \text{for } x > 1 \end{cases} \]

So, the correct answer is A.