Math Problem Statement

graph the function. Given the domain and range f(x)=xsquared+2

Solution

Here is the graph of the function f(x)=x2+2f(x) = x^2 + 2. The parabola has its vertex at (0,2)(0, 2), and it opens upwards. The domain is (,)(-\infty, \infty), and the range is [2,)[2, \infty).

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Related Questions:

  1. How would the graph change if the function were f(x)=x23f(x) = x^2 - 3?
  2. What is the effect of changing the constant 2 to 5 in f(x)=x2+5f(x) = x^2 + 5?
  3. How do you find the vertex of any quadratic function?
  4. What are the roots (if any) of the function f(x)=x2+2f(x) = x^2 + 2?
  5. How does the graph change if the coefficient of x2x^2 becomes negative?

Tip:

For any quadratic function f(x)=ax2+bx+cf(x) = ax^2 + bx + c, the vertex can be found using x=b2ax = -\frac{b}{2a}.

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Math Problem Analysis

Mathematical Concepts

Algebra
Functions
Quadratic Functions
Graphing

Formulas

f(x) = x^2 + 2
Domain: (-∞, ∞)
Range: [2, ∞]

Theorems

Vertex of a parabola
Quadratic function behavior

Suitable Grade Level

Grades 8-10