Math Problem Statement

The graph of part of linear function g is shown. What inequalities would represent the domain and range?

Solution

From the graph provided, we can identify the domain and range based on the x- and y-values where the line segment exists.

Domain:

The domain refers to all the x-values that the function covers. Based on the graph, the line segment starts around x=4x = -4 and ends at x=4x = 4.

Thus, the domain is: 4x4-4 \leq x \leq 4

Range:

The range refers to all the y-values that the function covers. The graph shows that the y-values span from y=4y = -4 (lowest point) to y=5y = 5 (highest point).

Thus, the range is: 4y5-4 \leq y \leq 5

If you'd like more details or have any questions, feel free to ask!


Here are 5 related questions to expand your understanding:

  1. How do we determine the slope of a linear function from a graph?
  2. What are the conditions for a function to have a finite domain and range?
  3. How does an open or closed dot affect inequalities in domain and range?
  4. Can a line segment represent a function, and how does that relate to the vertical line test?
  5. How would you write the equation of this line in slope-intercept form?

Tip: To determine the domain and range, always look for the leftmost and rightmost x-values for the domain, and the lowest and highest y-values for the range.

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Math Problem Analysis

Mathematical Concepts

Linear Functions
Inequalities
Domain and Range

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9