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

Question

(1 point)
Responses

y=⎧⎩⎨⎪⎪x+1, x≤−1x+2, −1<x<1x+3, x≥1
𝑦
=
{
𝑥
+
1
,

𝑥
≤
−
1
𝑥
+
2
,

−
1
<
𝑥
<
1
𝑥
+
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
=
{
𝑥
+
2
,

𝑥
<
−
1
𝑥
+
3
,

−
1
≤
𝑥
≤
1
𝑥
+
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, −1<x<1x+1, x≥1
𝑦
=
{
𝑥
+
2
,

𝑥
≤
−
1
𝑥
+
3
,

−
1
<
𝑥
<
1
𝑥
+
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 le

y=⎧⎩⎨⎪⎪x+2, x≤−1x+3, −1<x<1x+1, x≥1
𝑦
=
{
𝑥
+
2
,

𝑥
≤
−
1
𝑥
+
3
,

−
1
<
𝑥
<
1
𝑥
+
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+2, x≤1x+3, 2<x<4x+1, x≥2

Answer 1

To determine which of the given equations corresponds to the piecewise function shown in the graph, we must analyze the conditions and pieces of each proposed function.

Here's the breakdown of the options:

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

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

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

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

To identify the correct piecewise function, you would typically look at the behavior of the function at the specified points (-1 and 1 in particular) and whether the pieces match the slopes and y-intercepts indicated in the graph.

Assuming the graph depicts behavior consistent with linear segments jumping or transitioning at the x-values of -1 and 1, match the descriptions carefully to determine the correct option.

Based on a typical examination, the third option stands out as being most plausible: \[ y = \begin{cases} x + 2, & x \leq -1 \ x + 3, & -1 < x < 1 \ x + 1, & x \geq 1 \end{cases} \]

However, please confirm with the actual graph you have to ensure the condition statements match accordingly.