Question

Which of the following piecewise functions matches the graph? (1 point) Responses f(x)={2−x if x≤0, x−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)={−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−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)={x+5 if x≤−22x+3 if x>−2

Answer 1

To determine which piecewise function matches the graph, you'll need to analyze the characteristics of each function in the context of their intervals.

1. **Function 1:**
- \( f(x) = 2 - x \) if \( x \leq 0 \)
- \( f(x) = x - 5 \) if \( x > 0 \)
- This function decreases in the first part (for \( x \leq 0 \)) and then increases linearly from -5 when \( x = 0 \).

2. **Function 2:**
- \( f(x) = -5 \) if \( x < 0 \)
- \( f(x) = -x + 1 \) if \( x \geq 0 \)
- Here, the function is constant (\(-5\)) for \( x < 0\) and then increases linearly for \( x \geq 0\), starting from \(1\) when \( x = 0\).

3. **Function 3:**
- \( f(x) = -x - 1 \) if \( x < 1 \)
- \( f(x) = -x + 2 \) if \( x \geq 1 \)
- This function decreases until \( x = 1 \), then continues to decrease, but shifts upwards by 1.

4. **Function 4:**
- \( f(x) = x + 5 \) if \( x \leq -2 \)
- \( f(x) = 2x + 3 \) if \( x > -2 \)
- It increases with a slope of 1 before \( -2\) and also increases but with a different slope of 2 for \( x > -2\).

To determine which function matches the graph, you would need to compare the stated intervals and see where the graph intersects the coordinates at the transition points of the piecewise function.

Without the actual graph to refer to, I cannot specify which function matches the graph. However, you can analyze the interval behaviors above to match it with its corresponding graphical characteristics.

If you have the specific details or behaviors of the graph (like points of intersection or linearity), I can help you pinpoint the correct piecewise function.