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A coordinate plane with two lines, one with one open endpoint and one with a closed endpoint. The x-axis ranges from negative 5 to 10 and the y- axis ranges from negative 8 to 10. Both axes are in unit increments and are labeled in increments of 5.

Which of the following piecewise functions matches the graph?

(1 point)
Responses

f(x)={2−x if x≤0x−5 if x>0
f left parenthesis x right parenthesis equals left brace Start Rows 1st Row 2 minus x if x less-than-or-equal-to 0 2nd Row x minus 5 if x greater than 0 End Rows

f(x)={−x−1 if x<1−x+2 if x≥1
f left parenthesis x right parenthesis equals left brace Start Rows 1st Row negative x minus 1 if x less than 1 2nd Row negative x plus 2 if x greater-than-or-equal-to 1 End Rows

f(x)={−5 if x<0−x+1 if x≥0
f left parenthesis x right parenthesis equals left brace Start Rows 1st Row negative 5 if x less than 0 2nd Row negative x plus 1 if x greater-than-or-equal-to 0 End Rows

f(x)={x+5 if x≤−22x+3 if x>−2
f left parenthesis x right parenthesis equals left brace Start Rows 1st Row x plus 5 if x less-than-or-equal-to negative 2 2nd Row 2 x plus 3 if x greater than negative 2 End Rows
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1 answer

To determine which piecewise function matches the graph you've described, we need to consider the characteristics of the lines and their endpoints on the coordinate plane.

  1. The first piecewise function is: \[ f(x) = \begin{cases} 2 - x & \text{if } x \leq 0 \ x - 5 & \text{if } x > 0 \end{cases} \]

  2. The second piecewise function is: \[ f(x) = \begin{cases} -x - 1 & \text{if } x < 1 \ -x + 2 & \text{if } x \geq 1 \end{cases} \]

  3. The third piecewise function is: \[ f(x) = \begin{cases} -5 & \text{if } x < 0 \ -x + 1 & \text{if } x \geq 0 \end{cases} \]

  4. The fourth piecewise function is: \[ f(x) = \begin{cases} x + 5 & \text{if } x \leq -2 \ 2x + 3 & \text{if } x > -2 \end{cases} \]

To select the correct function based on the graph described (with one open endpoint and one closed endpoint), we would look at the characteristics of the lines at the endpoints:

  • If a function has a closed endpoint on one side, then that part of the function will include the value at that point.
  • If a function has an open endpoint, then it will not include the value at that point.

Given that we need more contextual information on the graph and the types of line segments (including their slopes and y-intercepts), I cannot definitively select from the options without analyzing the visual details.

However, since typical piecewise functions often involve examining the domain and behavior of the lines, you should check the slopes and intercepts of each piecewise function against the lines in your graph to find the match.

Please provide me with additional details or characteristics of the graph (such as the slope or the exact points where the lines intercept the axes) for me to assist you better!