Piecewise Linear Functions Quick Check

Question

5 of 55 of 5 Items

Question
Use the image to answer the question.

A coordinate plane's axes range from negative 10 to 10 by 1-unit increments. Two rays are plotted. The first ray starts from an open endpoint, while the second ray starts from a closed endpoint.

Choose the correct piecewise function.

(1 point)
Responses

y={−2, x>23, 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={−2, x>03, 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<03, 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

y={−2x3x

Answer 1

Based on your description of the coordinate plane with two rays, it sounds like you have two distinct segments for a piecewise function.

Since the first ray starts from an open endpoint and the second ray starts from a closed endpoint, we can interpret the conditions given for \( x \):

1. The first segment appears to be a constant value of \( -2 \).
2. The second segment appears to take the value \( 3 \).

Now let's analyze the function options given:

1. Option 1:

   • \( y = \begin{cases} -2, & x < 2 \ 3, & x \leq 3 \end{cases} \)
   • This does not match with the endpoint descriptions.

2. Option 2:

   • \( y = \begin{cases} -2, & x > 0 \ 3, & x < 0 \end{cases} \)
   • This does not match with the endpoint descriptions either.

3. Option 3:

   • \( y = \begin{cases} -2, & x < 0 \ 3, & x \geq 0 \end{cases} \)
   • This does not match with the endpoint descriptions as well.

4. Option 4:

   • \( y = \begin{cases} -2 & x < 3 \ 3 & x < 3 \end{cases} \)
   • This option seems incomplete and also doesn't clarify the conditions properly.

From your description, we need to correctly identify how the functions relate to the rays plotted on the graph. If the first ray goes to \( -2 \) from an open end and the second ray is at \( 3 \) from a closed end, the correct piecewise function could ideally have the following conditions:

Assuming the first segment \( y = -2 \) is valid for \( x \) approaching a certain value and the second segment \( y = 3 \) includes that value, we would write:

\[ y = \begin{cases} -2, & x < a \ 3, & x \geq a \end{cases} \]

Without knowing the specific positions for \( a \), it seems none of the provided options fully capture what you're describing.

If you refer to the ray's direction and specifically the conditions around \( x \) based on the evaluation of the plot, please ensure to provide further details or clarify the specific values of interest for a precise answer!