Math Problem Statement

Find the domain and the range of the function shown in the graph.

Solution

To find the domain and range of the function from the graph:

  1. Domain: The domain refers to the possible values of the input variable, which is time (days) on the horizontal axis.

    • From the graph, the time starts at 0 days and extends to 60 days. Therefore, the domain is:
      0x600 \leq x \leq 60 where xx represents time in days.
  2. Range: The range refers to the possible values of the output variable, which is the length of the road (in kilometers) on the vertical axis.

    • From the graph, the length of the road starts at 60 kilometers and increases to 240 kilometers. Therefore, the range is:
      60y24060 \leq y \leq 240 where yy represents the length of the road in kilometers.

Would you like more details or have any questions on this?

Here are some related questions:

  1. What does it mean if the domain is "all reals" in a function?
  2. How can we represent the domain and range on a number line?
  3. How do we determine domain and range from a table of values?
  4. What happens if the graph has breaks or undefined points?
  5. Can a function have a limited domain but an infinite range?

Tip: The domain represents all valid inputs (x-values), while the range represents all possible outputs (y-values) from the function.

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Math Problem Analysis

Mathematical Concepts

Functions
Domain and Range

Formulas

Domain: 0 ≤ x ≤ 60
Range: 60 ≤ y ≤ 240

Theorems

Basic function graph interpretation

Suitable Grade Level

Grades 7-9