Math Problem Statement

Use the graph of the function to find its domain and range. Write the domain and range in interval notation.

Solution

The graph shown represents a function with its domain and range in need of identification.

Domain:

The domain represents the set of all possible x-values (horizontal axis) that the function can take. From the graph:

  • The leftmost point on the curve appears to be at x=6x = -6, and the rightmost point is at x=5x = 5.
  • The point at x=6x = -6 is a closed point (filled in), meaning that 6-6 is included.
  • The point at x=5x = 5 is an open point (hollow), meaning that 55 is not included.

Thus, the domain in interval notation is: [6,5)[-6, 5)

Range:

The range represents the set of all possible y-values (vertical axis) that the function takes. From the graph:

  • The lowest point on the curve is at y=6y = -6, and the highest point is at y=7y = 7.
  • At y=6y = -6, the point is closed (included), and at y=7y = 7, the point is open (excluded).

Thus, the range in interval notation is: [6,7)[-6, 7)

Final Answer:

  • Domain: [6,5)[ -6, 5)
  • Range: [6,7)[ -6, 7)

Do you want more details or have any questions?

Here are 5 related questions you might want to explore:

  1. How do you determine if a point is open or closed on a graph?
  2. What is the significance of interval notation in calculus?
  3. How would the domain and range change if the graph extended further?
  4. Can a function have an infinite range or domain? What would that look like?
  5. How does continuity of the function affect its domain and range?

Tip: Closed intervals like [a,b][a, b] include the endpoints, while open intervals (a,b)(a, b) exclude them.

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Math Problem Analysis

Mathematical Concepts

Graphing
Functions
Domain and Range
Interval Notation

Formulas

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Theorems

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Suitable Grade Level

Grades 9-12