Determine the domain and range of the function without restrictions.

Does this answer make sense for this specific problem situation? Why or why not? (Example: Given the problem situation, it does not make sense to have negative numbers within the domain.)

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Step 4

If the domain and range does not make sense, determine the domain and range with restrictions.

A bird is building a nest in a tree 36 feet above the ground. The bird dropped a stick from the nest. The function f(x) = -16x² + 36 describes the height of the stick in feet after x seconds. Identify the domain and range of the function.

Food for Thought

1. What does the variable x represent in the function?

   Interactive popup. Assistance may be required. Check Your Answer The variable x represents the number of seconds after the stick is dropped from the nest.

2. According to the graph, at what height did the bird drop the stick?

   Interactive popup. Assistance may be required. Check Your Answer The bird drops the stick at 36 feet.

3. The points (-1, 20) and (2, -28) lie on the graph of the quadratic function f(x) = -16x² + 36. What do these points mean?

   Interactive popup. Assistance may be required. Check Your Answer The point (-1, 20) means at -1 second the stick is 20 feet above the ground. The point (2, -28) means at 2 seconds the stick is 28 feet below the ground.

Click on each step to see the process in determining the restrictions for this problem.

Read the problem and analyze the entire graph of the function f(x) = -16x² + 36.

Quadratic Functions, Rechneronline

Determine the domain and range of the function without restrictions. Use the answer box to drag and drop the correct answers into the correct location.

Does your answer make sense for this specific problem? Why or why not?

Interactive popup. Assistance may be required. Check Your Answer It does not make sense to include negative numbers within the domain because time cannot be negative. In addition, it does not make sense to include negative numbers within the range because the height of the stick does not extend below ground level.

If the domain and range does not make sense, determine the domain and range with restrictions. Use the answer box to drag and drop the correct answers into the correct location.

In summary, even though the graph of the function extends to other quadrants, the domain and range are restricted to quadrant 1 because negative numbers for time and height are not reasonable for this problem situation.