Question

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

(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

Answer 1

To determine the correct equation of the piecewise function from the given options, we need to identify the behavior of the function as defined in each piece and how the function is defined across different intervals of \( x \).

Let's break down each option based on the functions and intervals provided:

1. **First Option:**
\[
y =
\begin{cases}
x + 1 & x \leq -1 \\
x + 2 & -1 < x < 1 \\
x + 3 & x \geq 1
\end{cases}
\]
- For \( x \leq -1 \): \( y = x + 1 \)
- For \( -1 < x < 1 \): \( y = x + 2 \)
- For \( x \geq 1 \): \( y = x + 3 \)

2. **Second Option:**
\[
y =
\begin{cases}
x + 2 & x < -1 \\
x + 3 & -1 \leq x \leq 1 \\
x + 1 & x > 1
\end{cases}
\]
- For \( x < -1 \): \( y = x + 2 \)
- For \( -1 \leq x \leq 1 \): \( y = x + 3 \)
- For \( x > 1 \): \( y = x + 1 \)

3. **Third Option:**
\[
y =
\begin{cases}
x + 2 & x \leq -1 \\
x + 3 & -1 < x < 1 \\
x + 1 & x \geq 1
\end{cases}
\]
- For \( x \leq -1 \): \( y = x + 2 \)
- For \( -1 < x < 1 \): \( y = x + 3 \)
- For \( x \geq 1 \): \( y = x + 1 \)

To choose the correct piecewise function from the graph, one would have to check the actual graph lines and points matching the intervals specified in each option with the specific \( y \) values derived from the functions. If the graph includes values consistent with the second option or any one of the three options, that would determine the correctness.

Without the actual graph, one must rely on the general understanding of how the piecewise functions change across the specified domains.

If you provide me with the visual layout of the graph or specific characteristics, I would be more than happy to assist you in selecting the right piecewise function.