A part of linear function g is graphed on the grid.


 
Which inequalities best describe the domain and range of the part shown?
A.Domain:−7<x<6

Range:−4<g(x)<5

B.Domain:−7≤x≤6

Range:−4≤g(x)≤5

C. Domain:−4≤x≤5

Range:−7≤g(x)≤6

D.Domain:−4<x<5

Range:−7<g(x)<6



To determine the correct inequalities for the **domain** and **range** of the linear function \( g \) based on its graph, let's first clarify what domain and range represent:

1. **Domain**: The set of all possible \( x \)-values covered by the graph (the horizontal span).
2. **Range**: The set of all possible \( g(x) \)-values, which are the same as the \( y \)-values (the vertical span).

Assuming that we have the portion of the graph on hand, here's how we analyze it:

- **Domain**: The domain refers to the minimum and maximum \( x \)-values shown on the graph.
- **Range**: The range refers to the minimum and maximum \( g(x) \)-values (or \( y \)-values).

### Given Options:
Let's evaluate the choices one by one.

**A. Domain: \( -7 < x < 6 \), Range: \( -4 < g(x) < 5 \)**  
This indicates that the graph covers \( x \)-values from \( -7 \) to \( 6 \), but **not** including these endpoints, and \( y \)-values from \( -4 \) to \( 5 \), also excluding the endpoints.

**B. Domain: \( -7 \leq x \leq 6 \), Range: \( -4 \leq g(x) \leq 5 \)**  
This indicates that the graph covers \( x \)-values from \( -7 \) to \( 6 \), **including** these endpoints, and \( y \)-values from \( -4 \) to \( 5 \), including the endpoints as well.

**C. Domain: \( -4 \leq x \leq 5 \), Range: \( -7 \leq g(x) \leq 6 \)**  
This suggests that \( x \)-values are from \( -4 \) to \( 5 \), and \( y \)-values are from \( -7 \) to \( 6 \), both endpoints included. 

**D. Domain: \( -4 < x < 5 \), Range: \( -7 < g(x) < 6 \)**  
This suggests \( x \)-values are from \( -4 \) to \( 5 \), but endpoints are **not included**, and \( y \)-values from \( -7 \) to \( 6 \), also excluding endpoints.

### To choose the best answer:
- If the graph shows **solid dots** at the endpoints, it indicates that the endpoints are included, meaning the domain and range should have **"≤"** rather than strict inequality "<".
- If the graph shows **open dots**, the endpoints are **not included**, which would require strict inequalities ("<").

### Conclusion:
If the graph shows **closed dots at \( x = -7 \) and \( x = 6 \)** and similar for the \( y \)-values, the correct answer is **B.**

Otherwise, if the endpoints are not included, **A** would be correct.

Do you need more details or have any further questions?

### Related Questions:
1. How do you determine the domain from a graph?
2. How can you distinguish between closed and open intervals?
3. What is the difference between \( g(x) \) and \( f(x) \) in linear functions?
4. How do inequalities affect the graph of a linear function?
5. What is the impact of endpoint inclusion on real-world applications?

**Tip**: Always look for open or closed dots at the endpoints of a graph to decide whether the inequality includes the boundary points.

A part of linear function g is graphed on the grid. Which inequalities best describe the domain and range of the part shown?

Learn how to determine the domain and range of a linear function from its graph. This example explores various inequalities, endpoint inclusion, and graph interpretation. Suitable for students in Grades 8-10.

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