Find the domain and range y=x^2+2

Name: Problem 24, Chapter 1: Calculus Single Variable
Uploaded: 2021-04-30T16:45:21-08:00
Duration: 1 min 44 s
Channel: Gregory Higby
Description: Find the domain and range y=x^2+2

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Key Concepts

Function Transformations

Function transformations involve modifications applied to the basic form of a function, such as shifts, reflections, stretches, or compressions. A common transformation is a vertical shift, which adds or subtracts a constant to/from the function’s output, thereby affecting the range without altering the domain.

Quadratic Functions

Quadratic functions are polynomial functions of degree two and are generally expressed in the form ax^2 + bx + c. They have a parabolic graph that opens upward or downward depending on the coefficient a, and their analysis includes finding key features like the vertex, axis of symmetry, and intercepts, which are essential for determining the range.

Range

The range of a function is the set of all possible output values (typically y-values) that the function can produce. Determining the range often involves understanding how the function behaves, such as identifying minimum or maximum values and considering any shifts or transformations that affect the outputs.

Domain

The domain of a function refers to the complete set of possible input values (typically x-values) for which the function is defined. In many cases, such as with polynomials, the domain includes all real numbers because there are no restrictions on the inputs that can be used without causing undefined operations.

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