Question
Use the image to answer the question.
Two lines, a solid line and a dotted line, are drawn on a coordinate plane. Both the x-axis and y-axis range from negative 4 to 4 in 1-unit increments.
Create a piecewise function that represents the graph.
(1 point)
Responses
f(x)={1,2x−1,−3<x≤−1−1<x<1
f left parenthesis x right parenthesis equals left brace Start 2 by 2 Matrix 1st Row 1st Column 1 comma 2nd Column negative 3 less than x less-than-or-equal-to negative 1 2nd Row 1st Column 2 x minus 1 comma 2nd Column negative 1 less than x less than 1 End Matrix
f(x)={x+1,2x−1, −3≤x<−1−1≤x≤1
f left parenthesis x right parenthesis equals left brace Start 2 by 2 Matrix 1st Row 1st Column x plus 1 comma 2nd Column negative 3 less-than-or-equal-to x less than negative 1 2nd Row 1st Column 2 x minus 1 comma 2nd Column negative 1 less-than-or-equal-to x less-than-or-equal-to 1 End Matrix
f(x)={1,2x−1,−3≤x<−1−1≤x≤1
f left parenthesis x right parenthesis equals left brace Start 2 by 2 Matrix 1st Row 1st Column 1 comma 2nd Column negative 3 less-than-or-equal-to x less than negative 1 2nd Row 1st Column 2 x minus 1 comma 2nd Column negative 1 less-than-or-equal-to x less-than-or-equal-to 1 End Matrix
f(x)={1,2x, −3≤x<−1−1≤x≤1
Two lines, a solid line and a dotted line, are drawn on a coordinate plane. Both the x-axis and y-axis range from negative 4 to 4 in 1-unit increments.
Create a piecewise function that represents the graph.
(1 point)
Responses
f(x)={1,2x−1,−3<x≤−1−1<x<1
f left parenthesis x right parenthesis equals left brace Start 2 by 2 Matrix 1st Row 1st Column 1 comma 2nd Column negative 3 less than x less-than-or-equal-to negative 1 2nd Row 1st Column 2 x minus 1 comma 2nd Column negative 1 less than x less than 1 End Matrix
f(x)={x+1,2x−1, −3≤x<−1−1≤x≤1
f left parenthesis x right parenthesis equals left brace Start 2 by 2 Matrix 1st Row 1st Column x plus 1 comma 2nd Column negative 3 less-than-or-equal-to x less than negative 1 2nd Row 1st Column 2 x minus 1 comma 2nd Column negative 1 less-than-or-equal-to x less-than-or-equal-to 1 End Matrix
f(x)={1,2x−1,−3≤x<−1−1≤x≤1
f left parenthesis x right parenthesis equals left brace Start 2 by 2 Matrix 1st Row 1st Column 1 comma 2nd Column negative 3 less-than-or-equal-to x less than negative 1 2nd Row 1st Column 2 x minus 1 comma 2nd Column negative 1 less-than-or-equal-to x less-than-or-equal-to 1 End Matrix
f(x)={1,2x, −3≤x<−1−1≤x≤1
Answers
GPT-4o mini
To create the piecewise function, we can analyze the conditions based on the information given. The graph consists of two segments, and each segment has a different equation defined over specific intervals of \( x \).
Let's analyze the segments based on the standard intervals provided in the responses:
1. **First segment (for \( -3 \leq x < -1 \))**: this segment appears to represent a constant value. Based on the responses, it seems to be equal to either \( 1 \) or \( x + 1 \). However, without the visual accompaniment, we cannot ascertain which is correct.
2. **Second segment (for \( -1 \leq x \leq 1 \))**: this segment appears to be a linear function and is represented by \( 2x - 1 \) in some responses.
From this, we can determine that the likely piecewise function could be structured as follows:
- For \( -3 \leq x < -1 \), if we consider the first and second intervals:
- If the first segment was a constant value, it could be \( 1 \).
- For \( -1 \leq x \leq 1 \):
- A reasonable guess would be to take the linear function \( 2x - 1 \).
Putting these insights together from the response analysis, a reasonable piecewise function might be:
\[
f(x) =
\begin{cases}
1, & -3 \leq x < -1 \\
2x - 1, & -1 \leq x \leq 1
\end{cases}
\]
Based on the options given, if this corresponds to one of the initial choices, you would select that option to indicate your response.
Let's analyze the segments based on the standard intervals provided in the responses:
1. **First segment (for \( -3 \leq x < -1 \))**: this segment appears to represent a constant value. Based on the responses, it seems to be equal to either \( 1 \) or \( x + 1 \). However, without the visual accompaniment, we cannot ascertain which is correct.
2. **Second segment (for \( -1 \leq x \leq 1 \))**: this segment appears to be a linear function and is represented by \( 2x - 1 \) in some responses.
From this, we can determine that the likely piecewise function could be structured as follows:
- For \( -3 \leq x < -1 \), if we consider the first and second intervals:
- If the first segment was a constant value, it could be \( 1 \).
- For \( -1 \leq x \leq 1 \):
- A reasonable guess would be to take the linear function \( 2x - 1 \).
Putting these insights together from the response analysis, a reasonable piecewise function might be:
\[
f(x) =
\begin{cases}
1, & -3 \leq x < -1 \\
2x - 1, & -1 \leq x \leq 1
\end{cases}
\]
Based on the options given, if this corresponds to one of the initial choices, you would select that option to indicate your response.