Use the image to answer the question.

Question

Three lines, a solid line, a dotted line, and a dashed line, are drawn on a coordinate plane. The x-axis ranges from negative 4 to 4 in 1-unit increments, and the y-axis ranges from negative 3 to 5 in 1-unit increments.

Which option represents the piecewise function of the graph?

(1 point)
Responses

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 x less than negative 1 2nd Row 1st Column 3 x plus 1 comma 2nd Column negative 1 less than x less-than-or-equal-to 1 3rd Row 1st Column 1 comma 2nd Column 1 less than x less than 3 End Matrix

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

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

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
Skip to navigation

Answer 1

To determine which option represents the piecewise function of the graph, we need to analyze the conditions and equations given in each response.

1. First Response:

   • ( f(x) = \begin{cases} -2 & -3 < x < -1 \ 3x + 1 & -1 < x \leq 1 \ 1 & 1 < x < 3 \end{cases} )

2. Second Response:

   • ( f(x) = \begin{cases} -2 & x < -1 \ 3x + 1 & -1 \leq x < 1 \ 1 & 1 \leq x \end{cases} )

3. Third Response:

   • ( f(x) = \begin{cases} -2 & -3 \leq x < -1 \ 3x + 1 & -1 \leq x < 1 \ 1 & 1 \leq x \leq 3 \end{cases} )

4. Fourth Response:

   • ( f(x) = \begin{cases} -2 & -3 \leq x < -1 \ 3x + 1 & -1 \leq x < 1 \ x & 1 \leq x \leq 3 \end{cases} )

From this information:

• The first response has the inequalities which seem to limit some ranges incorrectly.
• The second response has an open interval for the first part, which should cover all points less than -1.
• The third response has the correct intervals for the function values involved and appropriate conditions for including the endpoints.
• The fourth response has an incorrect function value of \(x\) for the last segment where it should be just 1.

Given that we want to cover the ranges accurately based on the intersections/match of the graph pieces, the third response is the most likely correct representation of the piecewise function.

Thus, the answer is: f(x)=⎧⎩⎨⎪⎪−2,3x+1,1, −3≤x<−1−1≤x<11≤x≤3