Use the image to answer the question.

Question

Use the image to answer the question. Which of the following piecewise functions matches the graph? (1 point) Responses f(x)={−5 if x<0−x+1 if x≥0 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 ( 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)={−x−1 if x<1−x+2 if x≥1 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

GPT-4o mini · Answer

To determine which piecewise function matches the graph, typically you'd need to analyze the behavior of the function at the specified intervals and compare them to the characteristics of the graph presented.

However, without the actual image or graph to reference, I can help you outline how to analyze each option:

Examine the function for $x < 0$ and $x \geq 0$ for the first option. Check the constant value of -5 and the linear equation $- x + 1$ to see if they align with the graph.
For the second option, evaluate how the function behaves for $x \leq 0$ with $2 - x$ and how it transitions to $x - 5$ for $x > 0$ .
For the third option, observe how the function behaves below and above 1. Check if $- x - 1$ and $- x + 2$ make sense with the graph's slopes and intercepts around that value.
Check the last option as well, interpreting what the behavior of the function $x + 5$ indicates at different intervals.

Once you compare the line segments, slopes, and intercepts according to their proposed piecewise functions against the graph, you should be able to identify which option matches correctly. If you have specific features or values from the graph that you can describe, I can guide you further.