Choose the correct piecewise function.

Question

(1 point)
Responses

y={−2, x>03, x>0
𝑦
=
{
−
2
,



𝑥
>
0
3
,

𝑥
>
0
y equals left brace line 1 negative 2 comma x greater than 0 line 2 3 comma x less than 0

y={−2, x>23, x≤3
𝑦
=
{
−
2
,



𝑥
>
2
3
,

𝑥
≤
3
y equals left brace line 1 negative 2 comma x less than 2 line 2 3 comma x less than or equal to 3

y={−2x3x
𝑦
=
{
−
2
𝑥
3
𝑥
y equals left brace line 1 negative 2 time x line 2 3 times x

y={−2, x<03, x≥0
𝑦
=
{
−
2
,



𝑥
<
0
3
,

𝑥
≥
0
y equals left brace line 1 negative 2 comma x less than zero line 2 3 comma x less than or equal to zero

Answer 1

To identify the correct piecewise function from the options provided, we need to look for correct notation and conditions for the given values.

Here are the provided options in clearer formatting:

1. \[ y = \begin{cases} -2 & \text{if } x > 0 \ 3 & \text{if } x > 0 \end{cases} \]

2. \[ y = \begin{cases} -2 & \text{if } x > 2 \ 3 & \text{if } x \leq 3 \end{cases} \]

3. \[ y = \begin{cases} -2x & \ 3x & \end{cases} \]

4. \[ y = \begin{cases} -2 & \text{if } x < 0 \ 3 & \text{if } x \geq 0 \end{cases} \]

The correct piecewise function should have distinct conditions for each segment of the function without overlapping and should be properly defined for all cases.

The only option with correctly defined conditions is:

\[ y = \begin{cases} -2 & \text{if } x < 0 \ 3 & \text{if } x \geq 0 \end{cases} \]

Thus, the correct choice is the last option:

\[ y = \begin{cases} -2 & \text{if } x < 0 \ 3 & \text{if } x \geq 0 \end{cases} \]

Answer 2

pick one