Math Problem Statement

Find the domain and range of the function using the graph below.

Solution

From the graph, we can find the domain and range by identifying the x-values and y-values that the function covers.

Domain:

The domain of a function is the set of all possible x-values. The graph shows that the function starts at x=0x = 0 and goes to x=5x = 5. Therefore, the domain is: 0x50 \leq x \leq 5

Range:

The range is the set of all possible y-values. From the graph, the lowest y-value is y=2y = 2, and the highest y-value is y=6y = 6. Therefore, the range is: 2y62 \leq y \leq 6

Final Answer:

  • Domain: 0x50 \leq x \leq 5
  • Range: 2y62 \leq y \leq 6

Would you like more details on how domain and range are determined?


Here are 5 relative questions that extend this concept:

  1. What is the domain of a function that spans from x=3x = -3 to x=7x = 7?
  2. How would the range change if the highest point on the graph was at y=8y = 8?
  3. Can a function have an infinite domain or range? What does that look like?
  4. How do vertical and horizontal lines affect the domain and range?
  5. How does the concept of a "discrete" versus "continuous" graph change the interpretation of domain and range?

Tip: The domain represents the possible input values (x-axis), and the range represents the possible output values (y-axis).

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Math Problem Analysis

Mathematical Concepts

Functions
Domain and Range
Graphing

Formulas

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Theorems

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Suitable Grade Level

Grades 7-9