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 solve this problem, let’s first define the domain and range of a graphed function:

1. **Domain**: The set of all possible input values (x-values) for which the function is defined.
2. **Range**: The set of all possible output values (y-values, or g(x)) for the function.

For each option, the inequalities describe the domain and range.

- **Domain**: Refers to the interval of \(x\)-values (from left to right on the graph).
- **Range**: Refers to the interval of \(g(x)\) or \(y\)-values (from bottom to top on the graph).

### Let’s break down the options:
**A.** Domain: \( -7 < x < 6 \), Range: \( -4 < g(x) < 5 \)
- The inequalities in the domain and range are strict, meaning that the function does not include the endpoints.

**B.** Domain: \( -7 \leq x \leq 6 \), Range: \( -4 \leq g(x) \leq 5 \)
- The inequalities are inclusive, meaning the function includes the endpoints of the domain and range.

**C.** Domain: \( -4 \leq x \leq 5 \), Range: \( -7 \leq g(x) \leq 6 \)
- The domain and range appear reversed when compared to the rest.

**D.** Domain: \( -4 < x < 5 \), Range: \( -7 < g(x) < 6 \)
- Both domain and range use strict inequalities, and the intervals are reversed.

### Choosing the Correct Answer
Without the graph, option **B** seems the most reasonable as it includes the endpoint values, which is common in such questions. If the graph shows the function defined at those boundary points, then **B** is the best choice.

---

Let me know if you'd like further details or have any questions! Here are 5 related questions to explore:

1. How do you find the domain and range of a function from a graph?
2. What is the difference between strict and inclusive inequalities?
3. How do you find the domain and range of a linear function algebraically?
4. What is the significance of endpoint inclusion in a domain or range?
5. How would you represent a function with an infinite domain or range?

**Tip**: Always check if the endpoints are included in the graph to decide between strict (`<`) and inclusive (`≤`) inequalities.

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

Understand how to identify the domain and range of a linear function from its graph. This problem explores linear inequalities and provides key insights into strict and inclusive inequalities. Suitable for students in Grades 9-11.

Math Problem Statement

Solution

Ask a new question for Free

By Image

Math Problem Analysis

Mathematical Concepts

Formulas

Theorems

Suitable Grade Level

Related Recommendation