Math Problem Statement

What is the range of the function graphed below?

Solution

The graph shows a function that starts at y=2y = 2 and increases indefinitely as it moves to the right. This suggests that the function has a minimum yy-value of 2 and continues upward without bound. Therefore, the range of the function is:

[2,)[2, \infty)

This means that the yy-values begin at 2 and increase towards infinity.

Would you like further explanation or details on this? Here are five follow-up questions for you:

  1. What is the domain of this function based on the graph?
  2. How would you determine the domain and range for more complex functions?
  3. What types of functions have a range that extends to negative infinity?
  4. How does the behavior of the graph at x=0x = 0 affect its range?
  5. What does the range of a quadratic function typically look like?

Tip: To determine the range of any function, focus on the possible output values (or yy-values) it can take as xx varies.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Graphing

Formulas

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Theorems

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Suitable Grade Level

Grades 9-10