Math Problem Statement

Find the range and the domain of the function shown.

Solution

To find the domain and range of the function shown in the graph:

Domain:

  • The domain refers to all possible values of xx, which in this case is "Time (days)".
  • From the graph, the time starts at 00 days and ends at 9090 days.
  • Therefore, the domain is: {x0x90}\{x \mid 0 \leq x \leq 90\}

Range:

  • The range refers to all possible values of yy, which is the "Length of the road (kilometers)".
  • From the graph, the length starts at about 6060 kilometers and ends at about 150150 kilometers.
  • Therefore, the range is: {y60y150}\{y \mid 60 \leq y \leq 150\}

Would you like further details or have any other questions?

Here are 5 related questions to explore:

  1. How would the domain and range change if the graph extended to 120 days?
  2. What is the significance of the slope of this graph?
  3. How do you determine the domain and range from a non-linear graph?
  4. If the road construction rate increased, how would this affect the graph?
  5. How would you write the function that represents this graph?

Tip: When identifying domain and range, look at the start and end values of xx (for domain) and yy (for range) on the graph.

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Math Problem Analysis

Mathematical Concepts

Domain and Range
Graph Analysis
Linear Functions

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8