Math Problem Statement

What is the range of the function?

Solution

To solve this problem, let's break it down:

We are asked to find the range of the function shown by the graph. The range of a function refers to the set of all possible y-values (outputs) that the function can take.

Step-by-step analysis:

  1. Axes Understanding:

    • The x-axis represents the distance from a central point, while the y-axis represents the drone's height above the ground in meters.
  2. Graph Points:

    • From the graph, we can observe that:
      • The lowest point on the graph is at y=0y = 0 (the drone is at ground level).
      • The highest point on the graph is at y=4y = 4.
  3. Range Calculation:

    • Since the graph extends from y=0y = 0 to y=4y = 4, the range of the function includes all values from 0 to 4 meters.

Conclusion:

The range of the function is: [0,4]\boxed{[0, 4]}

Would you like more details or have any questions?

Here are some related questions to explore further:

  1. What is the domain of the function shown in the graph?
  2. How would you calculate the average rate of change of the function between two points?
  3. How do you find the intervals where the function is increasing or decreasing?
  4. What is the maximum value of the function, and at which x-value does it occur?
  5. How does the shape of this graph relate to real-world drone flight paths?

Tip: Remember, the range of a function is all the possible y-values, while the domain is the x-values.

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Math Problem Analysis

Mathematical Concepts

Functions
Graph interpretation

Formulas

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Theorems

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Suitable Grade Level

Grades 6-8