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Graphs and Functions

 f(x)=$\sqrt{x}$ g(x)=$\sqrt{x+3}$

Domain: The domain is all values that x can take on. The only problem you have with this function is that you cannot have a negative inside the square root. So you'll set the insides greater-than-or-equal-to zero, and solve.

Range: The range requires a graph.

Find the domain of f(x)=$\sqrt{15-2x-x^2}$
The expression under the radical has to satisfy the condition 15-2x-x2 > 0    for the function to take real values.

15-2x-x2 > 0
(5+x)(3-x) > 0
Evaluating at several points:

Then the domain is [-5,3]

Determine the domain of the given function:
$f(x)=sqrt{\frac{x+4}{-4x+12}}$
The domain is "all x"
The domain is "all x except the next point(s)"
The domain is given by the next intervals:

To use interval notation
: Write -i to get the symbol $-\infty$ and write i to get the symbol $\infty$