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)

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

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

1. f(x) = .

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

Figure 1

2. f(x) = .

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) = .

        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) = 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 everywhere where the last function is defined.

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