Question 1011693
.
Hello, I have a question regarding domain and range. When given a graph, how do you find the domain and range? Also, how do you set the domain and range into an inequality? 
---------------------------------------------------------------------

<pre>
The domain of a function is the set of numbers (real numbers) where the function is determined.

Examples:

f(x) = c              (constant).            The domain is the entire number line.

f(x) = ax + b         (linear function).     The domain is the entire number line.

f(x) = {{{ax^2 + bx + c}}}    (quadratic function)   The domain is the entire number line.

f(x) = {{{sqrt(x)}}}                                   The domain is the set of all non-negative numbers x > = 0.

f(x) = {{{sqrt(x+5)}}}                               The domain is the set of all real numbers x such that x+5 >= 0, i.e. x >= -5.

f(x) = {{{sqrt(ax^2 + bx + c)}}}                       The domain is the set of all real numbers x such that ax^2 + bx + c >= {{{0}}}.  
                                                So, in order to find the domain, you need to solve this inequality.

f(x) = {{{(x+1)/(x-2)}}}.                               The domain is the set of all real numbers except of x = 2: You can not divide by zero. It is prohibited.

There are the lessons on determining domains of functions in this site:

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Functions/Finding-domain-of-a-function.lesson>Domain of a function which involves a quadratic polynomial under the square root operator</A>,

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Functions/Domain-of-a-function-containing-high-degree-polynomial-under-the-square-root.lesson>Domain of a function containing high degree polynomial under the square root operator</A> &nbsp;and 

&nbsp;&nbsp;&nbsp;&nbsp;- <A HREF=http://www.algebra.com/algebra/homework/Functions/Domain-of-a-function-which-is-the-square-root-of-a-rat-function.lesson>Domain of a function which is the square root of a rational function</A> 
</pre>