Question
Use the image to answer the 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, 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,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
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+1,1, −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
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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, 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,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
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+1,1, −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
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Answers
There are no human answers yet.
Answered by
GPT-4o mini
To provide an accurate response to the question regarding the piecewise function of the graph represented by the three lines, I would need to analyze the specific characteristics of the lines shown in the image. Since I cannot see the image, I will base my response on the options provided.
Based on the common forms of piecewise functions, let's analyze each option:
1. **Option 1**: The function appears to break into three segments with specified domains. However, it includes `1 ≤ x`, which seems more likely to indicate a starting or ending point.
2. **Option 2**: Similar structure as Option 1 but with different specified bounds. This option also uses `1 ≤ x ≤ 3`, which suggests a closed interval.
3. **Option 3**: It also segments the function into three distinct parts, with the final piece ending at `3`, similar to Option 2, but states open and closed intervals differently.
4. **Option 4**: While it attempts to differentiate relationships for `x`, it has a few open intervals and closing statements that might not match typical definitions.
Without the visual context to know the slopes and specific ranges of the lines, I would advise looking at the specified segments. Typically, piecewise functions will have different slopes for different sections along the x-axis, and endpoints should be checked against whether they'll be filled (closed) or empty (open).
Based on common practice:
- If your solid line denotes a relation at endpoints, it would likely be represented in a closed interval.
- If a dotted or dashed line is used, that normally would indicate that the endpoints do not belong to that segment.
**Recommendation**: If you can clarify the characteristics of the lines or their slopes and their respective x-values, I will be able to help you select the correct option more accurately.
Based on the common forms of piecewise functions, let's analyze each option:
1. **Option 1**: The function appears to break into three segments with specified domains. However, it includes `1 ≤ x`, which seems more likely to indicate a starting or ending point.
2. **Option 2**: Similar structure as Option 1 but with different specified bounds. This option also uses `1 ≤ x ≤ 3`, which suggests a closed interval.
3. **Option 3**: It also segments the function into three distinct parts, with the final piece ending at `3`, similar to Option 2, but states open and closed intervals differently.
4. **Option 4**: While it attempts to differentiate relationships for `x`, it has a few open intervals and closing statements that might not match typical definitions.
Without the visual context to know the slopes and specific ranges of the lines, I would advise looking at the specified segments. Typically, piecewise functions will have different slopes for different sections along the x-axis, and endpoints should be checked against whether they'll be filled (closed) or empty (open).
Based on common practice:
- If your solid line denotes a relation at endpoints, it would likely be represented in a closed interval.
- If a dotted or dashed line is used, that normally would indicate that the endpoints do not belong to that segment.
**Recommendation**: If you can clarify the characteristics of the lines or their slopes and their respective x-values, I will be able to help you select the correct option more accurately.
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