Math Problem Statement

in interval notation

Solution

Here are the domain and range in interval notation:

Domain

The function is defined for all xx except at x=2x = 2. Therefore, the domain in interval notation is: (,2)(2,)(-\infty, 2) \cup (2, \infty)

Range

The function can take all yy values except at y=1y = 1. Therefore, the range in interval notation is: (,1)(1,)(-\infty, 1) \cup (1, \infty)

Would you like any details or have any questions?

Here are five more questions you might consider asking:

  1. How do you find the domain and range of a rational function?
  2. What is the significance of vertical asymptotes in determining the domain?
  3. Can a function have a range that includes all real numbers?
  4. How do horizontal asymptotes affect the range of a function?
  5. What are the steps to graphing a rational function?

Tip: When determining the range of a function, examine the vertical extent of the graph and look for any values that the function cannot reach.

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Math Problem Analysis

Mathematical Concepts

Functions
Domain and Range

Formulas

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Theorems

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Suitable Grade Level

High School