Question

Use the image to answer the 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.
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Select the equation of the piecewise function shown in the graph.

(1 point)

y=⎧⎩⎨⎪⎪x+2, x≤−1x+3, −1<x<1x+1, x≥1


y=⎧⎩⎨⎪⎪x+2, x≤1x+3, 2<x<4x+1, x≥2


y=⎧⎩⎨⎪⎪x+1, x≤−1x+2, −1<x<1x+3, x≥1


y=⎧⎩⎨⎪⎪x+2, x<−1x+3, −1≤x≤1x+1, x>1

Answer 1

y = { x + 2, x ≤ −1; x + 3, −1 < x < 1; x + 1, x ≥ 1 }

Justification: the left ray goes through (−2,0) and (−1,1) so y = x + 2 (closed at x = −1). The middle open segment goes through (0,3) so y = x + 3 on (−1,1). The right ray goes through (1,2) and (2,3) so y = x + 1 (closed at x = 1).