I Am Getting Confused on How To Find The Domain And Range Of Functions of a Graph.

For Example: f(x)=x^4-8x^2+8.

it has two min. points and one max point.

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- Sep 23rd 2008, 07:39 PM>_<SHY_GUY>_<[SOLVED] Domain
I Am Getting Confused on How To Find The Domain And Range Of Functions of a Graph.

For Example: f(x)=x^4-8x^2+8.

it has two min. points and one max point. - Sep 23rd 2008, 07:43 PMicemanfan
A function that is a single polynomial will have a domain of all real numbers. For the polynomial function you specified, you must compute the absolute minimum of the function in order to determine the range. The absolute minimum will be the smaller of the two local minima.

- Sep 23rd 2008, 07:45 PMJhevon
for a function of x:

the domain is the set of x-values for with the function is defined.

the range is the set of y-values for which the function is defined.

it is often easier to find the values for which a function is not defined, and say the domain or range is everything but that

with polynomials though, our lives are easy. polynomials are defined for all real x (unless we are restricting the domain with some additional condition).

for an even polynomial where the leading coefficient is positive, the range is $\displaystyle y \in [\text{absolute minimum}, \infty)$ - Sep 23rd 2008, 07:47 PM>_<SHY_GUY>_<
- Sep 23rd 2008, 07:52 PMLen
2a. Domain and Range of a Function

Quote:

**Domain:**The complete set of possible values of the independent variable in a function is called the**domain**of the function.

**In plain English**, the definition means:

The**domain**of a function is all the possiblevalues which will make the function "work" by outputting real values.**x**

When finding the**domain**, remember:

- denominator (bottom) of a fraction
**cannot be zero** - the values under a square root
**must be positive**

**Range:**The complete set of all possible resulting values of the dependent variable in a function is the*range*of the function.

**In plain English**, the definition means:

The**range**of a function is the possiblevalues of a function resulting when we substitute all the possible**y***x*-values.

When finding the**range**, remember:

- substitute different
*x*-values into the expression for*y*to see what is happening - make sure you look for
**minimum**and**maximum**values of**y** **draw**a**sketch!**

- denominator (bottom) of a fraction
- Sep 23rd 2008, 07:54 PMJhevon
- Sep 23rd 2008, 07:55 PM>_<SHY_GUY>_<
- Sep 23rd 2008, 07:56 PMJhevon
- Sep 23rd 2008, 07:58 PMJhevon
how are you confused?

no matter what x-values you plug in, the function works. you cover all x-values and so the domain is all real numbers. as for x^3, the function is continuous. one end goes to infinity, the other goes to minus infinity. you cover all y-values. so the domain is all real numbers. - Sep 23rd 2008, 07:58 PM>_<SHY_GUY>_<
in other words. if the graph shows the x-values growing continuously...then the range of a graph is all real

- Sep 23rd 2008, 08:04 PMicemanfan
Range can be tricky. Remember that for polynomials with real coefficients and odd degree, the range is all real numbers. For polynomials of even degree, you have to find the absolute minimum if the coefficient of the highest power of x is positive, or the absolute maximum if the coefficient of the highest power of x is negative.

- Sep 23rd 2008, 08:05 PMLen
The range is all possible values of y. Since you have said that -8 is the absolute minimum, there can be no values of y under -8 for any value of x.

Take the limit as x goes to positive and negative infinity. They both go to positive infinity. So like you said the range would be -8 to positive infinity. - Sep 23rd 2008, 08:08 PM>_<SHY_GUY>_<
- Sep 23rd 2008, 08:12 PMicemanfan
- Sep 23rd 2008, 08:17 PM>_<SHY_GUY>_<