# Finding the Domain and Range...

• Jan 29th 2007, 09:02 AM
hamnet
Finding the Domain and Range...
Hi :)

Can anyone tell me what is the easiest possible way to obtain the domain or range of a function? Also, how you would write down what you find from either a domain or a range? I am supposed to find the domain and range of any given function (quadratic, exponential, etc..), and state the both, or one or the other using mathlish.
• Jan 29th 2007, 09:51 AM
ticbol
Quote:

Originally Posted by hamnet
Hi :)

Can anyone tell me what is the easiest possible way to obtain the domain or range of a function? Also, how you would write down what you find from either a domain or a range? I am supposed to find the domain and range of any given function (quadratic, exponential, etc..), and state the both, or one or the other using mathlish.

What I know is
To find the domain of the function, find the values of the variable that will give a real range.
To find the range of the function, find the result when plugging or substituting the values of the variable that are in the domain in the function.

Mathlish? You mean in words?
Like, domain of f is all values of x from, but not including, x=2, up to x=6.
Domain is x = (2,6].
Domain is 2 < x <= 6. ----------I'm not sure of this.

I always like to state the domain in words. I am sometimes lost with all these many Math symbols.
• Jan 29th 2007, 10:13 AM
ThePerfectHacker
Quote:

Originally Posted by hamnet
Hi :)

Can anyone tell me what is the easiest possible way to obtain the domain or range of a function? Also, how you would write down what you find from either a domain or a range? I am supposed to find the domain and range of any given function (quadratic, exponential, etc..), and state the both, or one or the other using mathlish.

The way I find the range is a little dangerous, it involves a perfect understanding of what a function is, and I think many students will not be comfortable with it. The way I do it is find all $\displaystyle y$ such that the equation $\displaystyle y=f(x)$ has at least one solution in the domain of $\displaystyle f(x)$.
• Jan 29th 2007, 10:46 AM
hamnet
Is it true that "y" can never be a negative number? and "x" can be postive or negative?

Okay, if I was asked to find the domain and range, input the function in my TI-83, graphed it, and then opened the table of values... Let's say: the following functions:

y=2.1(0.75)^x... If I opened the table of values, for any value of "x", "y" is a positive number, I am guessing it goes to infinity without becoming a negative?

So.. what I am trying to ask is: for any value of "x" "y" must be greater than or equal to zero? or greater than zero?...

Let's say: y = .5x^2 - .5x - 10 ?????
• Jan 29th 2007, 03:59 PM
topsquark
Quote:

Originally Posted by hamnet
Is it true that "y" can never be a negative number? and "x" can be postive or negative?

Okay, if I was asked to find the domain and range, input the function in my TI-83, graphed it, and then opened the table of values... Let's say: the following functions:

y=2.1(0.75)^x... If I opened the table of values, for any value of "x", "y" is a positive number, I am guessing it goes to infinity without becoming a negative?

So.. what I am trying to ask is: for any value of "x" "y" must be greater than or equal to zero? or greater than zero?...

Let's say: y = .5x^2 - .5x - 10 ?????

Obviously the allowed y values for given x values depends on the function. What you have to do is look at the domain of the function and see what range values they generate. It is generally much easier to find a domain: just find what values would make the function an "unreal" or impossible value, then exclude them from the real line. That's your domain. The range is trickier, but you can generally intuit what the function is doing. TPH's method is nice in that it gives a way to easily find the range, but you need to be very careful with what you are doing to avoid problems.

Quote:

Originally Posted by hamnet
$\displaystyle y=2.1(0.75)^x$

There are no restrictions on x here, so the domain is $\displaystyle (-\infty, \infty)$. Yes, the range is $\displaystyle (0, \infty)$

Quote:

Originally Posted by hamnet
$\displaystyle y = .5x^2 - .5x - 10$

There are no restrictions on x here, so the domain is $\displaystyle (-\infty, \infty)$. The function has a minimum value (vertex point) at $\displaystyle (x, y) = \left ( \frac{1}{2}, -\frac{81}{8} \right )$, so the range will be $\displaystyle \left ( -\frac{81}{8}, \infty \right )$.

-Dan