Question

Select the equation of the piecewise function shown in the graph. (1 point) Responses 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 y equals left brace line 1 x plus 1, x is less than or equal to negative 1 line 2 x plus 2 comma negative 1 less than x less than 1 line 3 x plus 3 comma x greater than or equal to 1 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 Skip to navigation

Answer 1

To determine the correct equation for the piecewise function based on the given options, we need to analyze the definitions of the functions along with their specified intervals.

Let's break down the responses provided:

1. Response 1: \[ y = \begin{cases} x + 2, & x \leq 1 \ x + 3, & 2 < x < 4 \ x + 1, & x \geq 2 \end{cases} \]

2. Response 2: \[ y = \begin{cases} x + 2, & x \leq -1 \ x + 3, & -1 < x < 1 \ x + 1, & x \geq 1 \end{cases} \]

3. Response 3: \[ y = \begin{cases} x + 1, & x \leq -1 \ x + 2, & -1 < x < 1 \ x + 3, & x \geq 1 \end{cases} \]

4. Response 4: \[ y = \begin{cases} x + 2, & x < -1 \ x + 3, & -1 \leq x \leq 1 \ x + 1, & x > 1 \end{cases} \]

To select the correct response, check for the following characteristics in the graph (if available):

• The slope and constant term of each segment where the function changes its definition.
• The intervals where each piece is applicable and whether they include or exclude endpoints.

Since the graph is not available here, you will need to match the pattern evident in the graph with one of the responses listed. If, for instance:

• The first segment appears linear, starting at a certain y-intercept leading up to a point where it changes.
• The second segment has a different slope or change.

Based on this, select the correct piece of the function, ensuring to examine the endpoints carefully.

In absence of the graph, you would need to have information relating to which segments cover what values. Please provide further details if you need specific help identifying characteristics corresponding to the graph!