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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)={−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)={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+5 if x≤−22x+3 if x>−2

answer with what I provided you

1 answer

Based on the description you provided, it appears the graph has two lines with one having an open endpoint and the other with a closed endpoint.

Let's analyze the options given:

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

  2. Option 2: \[ f(x) = \begin{cases} -5 & \text{if } x < 0 \ -x + 1 & \text{if } x \geq 0 \end{cases} \]

  3. Option 3: \[ f(x) = \begin{cases} 2 - x & \text{if } x \leq 0 \ x - 5 & \text{if } x > 0 \end{cases} \]

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

To match the piecewise functions with the characteristics of the lines described (one open endpoint, one closed endpoint), we need to determine their behaviors at boundary points and endpoints.

Since you described the lines and their properties but didn't provide any specific details about their slopes, positions, or intercepts, I'll look generally:

  • Open vs. Closed Endpoint: This will typically indicate whether the line reaches its endpoint or not. We should expect a transition in the function where one rule ends and another begins without including the boundary point.
  • Positive and Negative Slope: Checking the slopes in the equations might also guide us in understanding if one function matches the downward trend or upward trend you suggest.

Without a visual, it's tough to conclude definitively, but based on the details, one would analyze and see if the slopes indicated fit your description of lines having the necessary continuity and restrictions. If the description leans heavily towards one of the equations fitting the transition and continuity of slopes without major discontinuities, you could suggest that.

Given that there’s a possibility that the first line's open endpoint and the second line's closed endpoint relate closely to common piecewise functions used, I would recommend confirming visually with observed slopes.

If directly answering from a known context:

  • The correct piecewise function could potentially be Option 3, as it accounts for continuity across a boundary at \( x = 0 \) in a way that can reflect the transitions noted provided the slopes were distinctly expressed.

You will need to review and confirm graphically these relationships fit what you’ve observed ideally!