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The solid line starts with an open circle at left parenthesis 1 comma 4 right parenthesis and ends with a closed circle at left parenthesis negative 1 comma negative 2 right parenthesis. The dotted line starts with a closed circle at left parenthesis negative 1 comma negative 2 right parenthesis and ends with a closed circle at left parenthesis negative 3 comma negative 2 right parenthesis. The dashed line starts with a closed circle at left parenthesis 1 comma 1 right parenthesis and ends with a closed circle at left parenthesis 3 comma 1 right parenthesis.


Which option represents the piecewise function of the graph?

(1 point)
Responses

1. f(x)=⎧⎩⎨⎪⎪−2.3x+1,1, x<−1−1≤x<11≤x

f left parenthesis x right parenthesis equals left brace Start 3 by 2 Matrix 1st Row 1st Column negative 2 comma 2nd Column x less than negative 1 2nd Row 1st Column 3 x plus 1 comma 2nd Column negative 1 less-than-or-equal-to x less than 1 3rd Row 1st Column 1 comma 2nd Column 1 less-than-or-equal-to x End Matrix

2. f(x)=⎧⎩⎨⎪⎪−2,3x+1,x, −3≤x<−1−1≤x<11≤x≤3

f left parenthesis x right parenthesis equals left brace Start 3 by 2 Matrix 1st Row 1st Column negative 2 comma 2nd Column negative 3 less-than-or-equal-to x less than negative 1 2nd Row 1st Column 3 x plus 1 comma 2nd Column negative 1 less-than-or-equal-to x less than 1 3rd Row 1st Column x comma 2nd Column 1 less-than-or-equal-to x less-than-or-equal-to 3 End Matrix

3. f(x)=⎧⎩⎨⎪⎪−2,3x+1,1, −3≤x<−1−1≤x<11≤x≤3

f left parenthesis x right parenthesis equals left brace Start 3 by 2 Matrix 1st Row 1st Column negative 2 comma 2nd Column negative 3 less-than-or-equal-to x less than negative 1 2nd Row 1st Column 3 x plus 1 comma 2nd Column negative 1 less-than-or-equal-to x less than 1 3rd Row 1st Column 1 comma 2nd Column 1 less-than-or-equal-to x less-than-or-equal-to 3 End Matrix

4. f(x)=⎧⎩⎨⎪⎪−2,3x+1,1, −3<x<−1−1<x≤11<x<3

All Answers 1

Answered by GPT-5 mini AI
Option 3.

Reason: The horizontal piece from x = -3 to -1 is y = -2; the line through (-1,-2) and (1,4) has slope 3 and equation y = 3x + 1 for -1 ≤ x < 1; the top horizontal piece from x = 1 to 3 is y = 1. So
f(x) = { -2 for -3 ≤ x < -1; 3x + 1 for -1 ≤ x < 1; 1 for 1 ≤ x ≤ 3 } which is option 3.