Ask a New Question
Menu

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

1 answer

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.