Math Problem Statement

what's the range and the domain

what's the range and the domain?

Solution

Looking at the graph you provided, which is a parabola, I can determine the domain and range.

  1. Domain: The domain represents the set of all possible xx-values for which the function is defined. From the graph, the parabola starts at x=2x = 2 and ends at x=6x = 6. So the domain is:

    Domain:[2,6]\text{Domain}: [2, 6]

  2. Range: The range represents the set of all possible yy-values that the function can take. The lowest point of the parabola is at y=0y = 0, and the highest points are at y=4y = 4, which is at both x=2x = 2 and x=6x = 6. So the range is:

    Range:[0,4]\text{Range}: [0, 4]

Let me know if you'd like further details on interpreting such graphs!

Here are some relative questions:

  1. How would the domain change if the parabola extended further in both directions?
  2. How would the range change if the vertex of the parabola moved up or down?
  3. What does the vertex of the parabola represent in terms of the function?
  4. How would you describe a parabola that opens downward instead of upward?
  5. Can the domain of a function ever be restricted in real-world problems?

Tip: Always remember that the domain of a function tells you the valid inputs, and the range tells you the possible outputs.

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Math Problem Analysis

Mathematical Concepts

Functions
Quadratic Functions
Graphing Parabolas

Formulas

Domain: Set of possible x-values
Range: Set of possible y-values

Theorems

Properties of Parabolas
Graphing Quadratic Functions

Suitable Grade Level

Grades 7-10