Select the equation of the piecewise function shown in the graph.

Question

(1 point)
Responses

y=⎧⎩⎨⎪⎪x+2, x<−1x+3, −1≤x≤1x+1, x>1
y equals left brace line 1 x plus 2, x is less than negative 1 line 2 x plus 3 comma negative 1 less than or equal to x less than or equal to 1 line 3 x plus 1 comma x greater than 1

y=⎧⎩⎨⎪⎪x+2, x≤1x+3, 2<x<4x+1, x≥2
y equals left brace line 1 x plus 2, x is less than or equal to negative 1 line 2 x plus 3 comma 2 less than x less than 4 line 3 x plus 1 comma x greater than or equal to 2

y=⎧⎩⎨⎪⎪x+2, x≤−1x+3, −1<x<1x+1, x≥1
y equals left brace line 1 x plus 2, x is less than or equal to negative 1 line 2 x plus 3 comma negative 1 less than x less than 1 line 3 x plus 1 comma x greater than or equal to 1

y=⎧⎩⎨⎪⎪x+1, x≤−1x+2, −1<x<1x+3, x≥1

Answer 1

To accurately select the equation of the piecewise function that corresponds to the provided graph, I would need to have visibility of the graph itself in order to determine the correct segments and their corresponding conditions.

However, I can provide guidance on how to analyze the piecewise function options:

1. Identify Key Points: Look at the graph for values where the function changes (these points typically occur at x-values such as -1, 0, and 1).

2. Check the Function Behaviors: Determine what the output value of the function is at each section:

   • For \(x < -1\) (check the behavior of the function left of -1).
   • For \(-1 \leq x \leq 1\) (look at the trend of the graph or output value from -1 to 1).
   • For \(x > 1\) (observe the behavior of the function right of 1).

3. Select Matching Option: Compare the behavior and output you observed in the graph with the options given.

Based on your general response layout, here is how you might categorize the provided options:

• The first option suggests the following segments:

  • \( y = x + 2 \) for \( x < -1 \)
  • \( y = x + 3 \) for \( -1 \leq x \leq 1 \)
  • \( y = x + 1 \) for \( x > 1 \)

• The other options contain variations of these segments. For example:

  • The second option includes conditions for \( x \) values such as \( x \leq -1 \), \( 2 < x < 4 \), and \( x \geq 2\) which seems unrelated to the common points previously discussed.

To conclude, if you can visually identify the behavior of the function across the critical points and compare those observations to the mathematical expressions given in each response choice, you should be able to select the correct piecewise representation. If you need help with specific behaviors or intervals, feel free to describe the graph in more detail or share key points and outputs!