Domain Estimated Value

Monday, April 6th, 2009 at 3:41 pm

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Domain Estimated Value

math story problem?

Car tires need to be inflated properly. Overinflation or underinflation can cause premature treadwear. The table below shows tire life for different inflation values for a certain type of tire.

Pressure (lb/in squared) , Tire Life (1000 mi)
26 , 50
28 , 66
31 , 78
33 , 81
38 , 74
42 , 70
43 , 59

1. Make a graph of the data. Use the inflation values as independent variables and increments of 5lb/in squared on that axis. Use increments of 10,000 miles on the vertical axis.

2. What is the domain of this function?

3. What is the range of this function?

4. Use the graph to estimate the pressure that gives the longest tire life.

5. When does the tire life start to decrease?

Hi,

If you enter this data into a graphing calculator, it can approximate the line of best fit as a quadratic function y = -.35x² + 24.6x - 350.6. Use a graphing calculator to graph this.

The domain of this function would be restricted to the only values that make any sense, those points with a positive y value. That means the domain is (19.87,50.49) so air pressure must be between 19.87 and 50.49 lb/in².

The range of this function would be restricted to the only values that make any sense, points with a non-negative y value. That means the range is (0,81949).

The maximum y value occurs at (35.18,81949) so a tire pressure of 35.18 lb/in² gives the maximum tire life of 81,949 miles.

Tire life starts to decrease if air pressure is less than 35.18 lb/in² or if it's more than 35.18 lb/in².

I hope that helps!!