Question

One of the two rays starts from a closed endpoint located in the first quadrant at left parenthesis 1 comma 2 right parenthesis. This ray diagonally extends upward and rightward through left parenthesis 2 comma 3 right parenthesis and left parenthesis 4 comma 5 right parenthesis to stay in the first quadrant. The other ray starts from a closed endpoint located in the second quadrant at left parenthesis negative 1 comma 1 right parenthesis. This ray extends diagonally leftward and downward through the second and fourth quadrants and beyond. It passes through left parenthesis negative 2 comma 0 right parenthesis and left parenthesis negative 4 comma negative 2 right parenthesis. The line segment has one open endpoint at left parenthesis 1 comma 4 right parenthesis and the other open endpoint at left parenthesis negative 1 comma 2 right parenthesis. The open endpoints are connected by a diagonally extended, dotted line that passes through left parenthesis 0 comma 3 right parenthesis. The line segment passes through the second and first quadrants.


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

(1 point)
Responses

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, −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+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

Answer 1

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

Reason: left ray through (−1,1), (−2,0) is y = x+2 (closed at x = −1); middle open segment through (−1,2),(0,3),(1,4) is y = x+3 for −1<x<1; right ray through (1,2),(2,3) is y = x+1 (closed at x = 1).