(male narrator)

In this video, we’re going to begin

taking a look at what is called

the “domain of a function.” Domain is simply a list

of all the possible… input… or x-values. In other words,

a domain is a list of what numbers we are allowed

to plug into a function without making

the function undefined. There are two types of functions

that we should be aware of that can create

an undefined situation. One of the key ones

is a fraction. In fractions, it is

important to remember that what is not allowed

to occur is that the denominator… can’t…be…0. If the denominator

ends up being 0, the function

would be undefined. Another situation we must be

aware of is even radicals. If the index is even, what is

inside cannot be negative. It must be greater than

or equal to 0. We can’t take an even root

of a negative number. This would make

the function undefined. Let’s try some examples

where we find the domain or list what values keep the

function from being undefined. In this problem, while there

are several things occurring, what is interesting to us

is the 4th root. The multiplying by 3

doesn’t interest us as much– as we can multiply

any number by 3, and we can add 4

to any numbers. There’s

no restrictions. But we do have a restriction

on a 4th root, and that is the stuff

inside the radical. The 2x minus 6

can’t be negative. It must be greater than

or equal to 0. Solving this equation

by adding 6 to both sides, giving us 2x is greater than

or equal to 6, and then dividing by 2, gives us the domain

of the function to be x is greater than

or equal to 3. In other words, we’re saying that any value

greater than or equal to 3, when plugged in for x,

will give us a real solution. If we pick a number smaller

than 3 and plug it in for x, we’ll end up with a negative

value under the root, which makes the function

undefined. Let’s take a look

at another example. In this problem, we have

several things happening, but notice,

as we look for restrictions

on what happens, we can multiply

any number by 2. We can add 7

to any number. We can take the absolute value

of any number. We can also square

any number. We can multiply

anything by 3, and we can subtract 4

from anything. As we look through the

operations in this function, there are no restrictions

that are not allowed to occur. Because there are

no restrictions on the domain

or the input value, we say the domain here

is all real numbers. In other words,

any number you plug in for x will make this equation

a true equation… that has

no undefined points. Let’s try

one more example. This problem’s

a fraction. You may remember with fractions,

the denominator cannot equal 0. With fractions, the numerator

can be anything it wants, and so, when we’re looking

for the domain, we don’t really care

about the numerator. When we’re looking

for domain, we’re gonna focus

on the denominator and find out

when it equals 0. We can quickly find this

by factoring to x, minus 2, times x, plus 1,

knowing that cannot equal 0. Setting each factor

equal to 0– x minus 2, equals 0;

and x plus 1, equals 0– we can quickly solve

by adding 2 to get x equals 2, and subtracting 1

to get x equals -1. We’ll say that x cannot equal 2,

and x cannot equal -1. Because if we were to plug

those values into this function, we would end up

with 0 in the denominator, and that would be

undefined. Domain is a list of what keeps

the function defined, whether we’re saying

what x does not equal or whether we’re saying

what x is greater than.

## One Comment

## Steven Dowling Jr

I imagine your cat knocked the mic over at 0:30 ðŸ˜€