SOLUTION: Find the domain and range and graph the following functions. 1. f(x)=5-x^2 2. f(x)={{{sqrt(4-x^2)}}} 3. f(x)=(x^2-4)/(x-2)

Algebra ->  Functions -> SOLUTION: Find the domain and range and graph the following functions. 1. f(x)=5-x^2 2. f(x)={{{sqrt(4-x^2)}}} 3. f(x)=(x^2-4)/(x-2)       Log On


   

Question 987543: Find the domain and range and graph the following functions.
1. f(x)=5-x^2
2. f(x)=sqrt%284-x%5E2%29
3. f(x)=(x^2-4)/(x-2)

Answer by ikleyn(52797) About Me  (Show Source):
You can put this solution on YOUR website!

1.  f(x) = 5-x%5E2.

        The domain is the set of all real numbers  (the entire number line).                        
        The range is the set of all real numbers  x <= 5.

graph%28+240%2C+160%2C+-5.5%2C+5.5%2C+-4.5%2C+6.5%2C%0D%0A++++++++++5+-+x%5E2%0D%0A%29

            Figure 1


2.  f(x) = sqrt%284-x%5E2%29.

        The domain is the set of real numbers  -2 <= x <=2.  It is the segment  [-2, 2].        
        The range is the set of real numbers  0 <= x <= 2.



            Figure 2

3.  f(x) = %28x%5E2-4%29%2F%28x-2%29.

        The domain is the set of real numbers except of  x = 2,  where the denominator is equal to zero.
        The range is the set of all real numbers  (the entire number line).

        Notice that  f(x) = x+%2B+2  everywhere except of  x = 2, where it is formally not defined.
        If you define  f(x) = 0  at  x = 2,  then you will get a continuous function  y = x+2  which coincides with  %28x%5E2-4%29%2F%28x-2%29 everywhere where the last function is defined.