Domain

Example 1

Find the domain of h = { (3, 4), (5, 4), (6, 1), (7, 3), (9, 0), (10, -2)}

Solution .

The domain is the set of all first coordinates which in this case is {3, 5, 6, 7, 9, 10}

Example 2

Find the domain of the function given by

Solution .

We take the largest set of x values for which this equation makes sense. Since we cannot divide by zero, we exclude where . Because this is equivalent to we must exclude x = 2 and x = 3. Thus, the domain is all real numbers except for x =2 and x = 3.

Example 3

In a rectangle the width and the length total 50 feet. Express the area of the rectangle as a function of its width and find the domain of this function.

Solution .

Because A = LW and we want A only in terms of W, we must find a way of writing L in terms of just W. Since L + W = 50, L = 50 - W. As a result, or

If we looked at this formula out of context, we'd say that the domain would be all real numbers. However, in this case, we know that W is width so W>0. Since L = 50 - W and L must also be positive, W must be less than 50. Consequently the domain implied in this problem is 0<W<50.

The table below shows what would happen to area, A, if we let W be nonnegative or 50 or more.

 W             A(W)     

--------------------------

-10.          -600.       

-5.000000000  -275.0000000

0             0           

5.00000000    225.0000000 

10.00000000   400.0000000 

15.00000000   525.0000000 

20.00000000   600.0000000 

25.00000000   625.0000000 

30.00000000   600.0000000 

35.00000000   525.000000  

40.00000000   400.000000  

45.00000000   225.000000  

50.00000000   0           

55.00000000   -275.000000 

60.00000000   -600.000000