Math Problem Statement

y=(×+2)^2-3 find the domain of the function

Solution

The function given is y=(x+2)23y = (x + 2)^2 - 3.

Finding the Domain:

The domain of a function is the set of all possible input values (usually xx-values) for which the function is defined.

For the function y=(x+2)23y = (x + 2)^2 - 3, there are no restrictions on xx. This is because:

  • The function involves a squared term, (x+2)2(x + 2)^2, which is defined for all real numbers.
  • Subtracting 3 does not impose any additional restrictions.

Thus, the domain of the function is all real numbers.

Domain in Set Notation:

Domain: x(,)\text{Domain: } x \in (-\infty, \infty)

Would you like more details or have any questions?

Here are some related questions:

  1. What is the range of the function y=(x+2)23y = (x + 2)^2 - 3?
  2. How do you find the vertex of the parabola described by this function?
  3. What is the axis of symmetry for the function y=(x+2)23y = (x + 2)^2 - 3?
  4. How does the graph of y=(x+2)23y = (x + 2)^2 - 3 compare to the graph of y=x2y = x^2?
  5. How can you determine the intercepts of the function y=(x+2)23y = (x + 2)^2 - 3?

Tip: The domain of a polynomial function is always all real numbers unless the function includes a fraction or a square root.

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Math Problem Analysis

Mathematical Concepts

Functions
Quadratic Equations
Domain

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12