Math Problem Statement

Which inequality best describes the range of the function below?

Solution

Let's analyze the graph in the image to determine the correct inequality describing the range of the function.

Observations:

  • The function is a straight line starting from a closed point at y=2y = -2 (on the left side) and extending to an open point at y=2y = 2 (on the right side).
  • The line increases linearly from y=2y = -2 to y=2y = 2.
  • Since the point at y=2y = -2 is closed, the value y=2y = -2 is included in the range, whereas y=2y = 2 is not included because of the open point.

Range of the function:

The range of the function includes all values of yy between 2-2 and 22, including 2-2 but not 22.

Thus, the correct inequality that describes the range is: 2y<2-2 \leq y < 2

This corresponds to the third option:

  • 2y<2-2 \leq y < 2

Would you like more details or further clarification? Here are some related questions you might consider:

  1. How do you find the domain of a function from its graph?
  2. What does an open versus closed point indicate about a function's range?
  3. Can a function have the same domain and range? Under what circumstances?
  4. What is the difference between the domain and the range of a function?
  5. How does the slope of a line affect the range of a linear function?

Tip: Always pay attention to open and closed points on a graph—they indicate whether boundary values are included or excluded in the domain or range.

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Math Problem Analysis

Mathematical Concepts

Functions
Range of Functions
Linear Inequalities

Formulas

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Theorems

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Suitable Grade Level

Grade 8-10