Graphs
Area Problems
Example Continued
Step 3.Rewrite the equation using x and y variables and graph using a graphing calculator.
Step 4. Answer the questions.
- What is the domain?
- Since the inputs are based on width, the domain is all real numbers greater than or equal to 0;
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- Since the inputs are based on width, the domain is all real numbers greater than or equal to 0;
- What is the range?
- Since the outputs are based on area, the range is all real numbers greater than or equal to 0;
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- Since the outputs are based on area, the range is all real numbers greater than or equal to 0;
- For what values of l is the area zero?
- This question is asking for the output to be zero, in other words the x-intercepts, which are (0, 0) and (0, 400).
- For what value of l is there a maximum area?
- This question is asking for the maximum value, in other words the vertex, which is (200, 80,000). The value of l that results in the maximum area is 200 feet.