Math Problem Statement

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

Solution

To determine the correct inequalities describing the domain and range of the given graph of the linear function gg, let’s analyze the graph step-by-step:

Domain Analysis:

  • The domain represents all possible xx-values of the function.
  • From the graph, the line starts at the point (7,4)(-7, -4) and ends at the point (6,5)(6, 5).
  • Therefore, the domain of the function is 7x6-7 \leq x \leq 6.

Range Analysis:

  • The range represents all possible yy-values of the function.
  • From the graph, the lowest point is (7,4)(-7, -4) and the highest point is (6,5)(6, 5).
  • Thus, the range of the function is 4g(x)5-4 \leq g(x) \leq 5.

Correct Answer:

  • The inequalities that best describe the domain and range are:
    • Domain: 7x6-7 \leq x \leq 6
    • Range: 4g(x)5-4 \leq g(x) \leq 5

This matches the selected answer:

  • Domain: 7x6-7 \leq x \leq 6
  • Range: 4g(x)5-4 \leq g(x) \leq 5

Would you like further details or have any questions?

Related Questions:

  1. How do you determine the domain and range from a graph?
  2. What is the importance of understanding the domain and range of a function?
  3. How can you express domain and range using interval notation?
  4. What other types of functions have specific domains and ranges?
  5. How does the slope of a line affect the range of a function?

Tip:

Always pay close attention to the endpoints of a graph when determining the domain and range, especially whether the points are included or excluded (open or closed circles).

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Domain and Range

Formulas

Domain of a function: All possible x-values
Range of a function: All possible y-values

Theorems

Graphing of Linear Functions
Domain and Range determination from a graph

Suitable Grade Level

Grades 7-10