The function f of x is graphed. What is its domain? So the way it’s graphed

right over here, we could assume that this

is the entire function definition for f of x. So for example, if

we say, well, what does f of x equal when x

is equal to negative 9? Well, we go up here. We don’t see it’s graphed here. It’s not defined for x

equals negative 9 or x equals negative 8 and 1/2 or

x equals negative 8. It’s not defined for

any of these values. It only starts getting defined

at x equals negative 6. At x equals negative 6,

f of x is equal to 5. And then it keeps

getting defined. f of x is defined for x all

the way from x equals negative 6 all the

way to x equals 7. When x equals 7, f

of x is equal to 5. You can take any x value

between negative 6, including negative

6, and positive 7, including positive

7, and you just have to see– you

just have to move up above that number,

wherever you are, to find out what the value of

the function is at that point. So the domain of this

function definition? Well, f of x is

defined for any x that is greater than or

equal to negative 6. Or we could say negative 6

is less than or equal to x, which is less than

or equal to 7. If x satisfies this

condition right over here, the function is defined. So that’s its domain. So let’s check our answer. Let’s do a few more of these. The function f of x is graphed. What is its domain? Well, exact similar argument. This function is not defined

for x is negative 9, negative 8, all the way down or all the way

up I should say to negative 1. At negative 1, it

starts getting defined. f of negative 1 is negative 5. So it’s defined for negative

1 is less than or equal to x. And it’s defined all the

way up to x equals 7, including x equals 7. So this right over

here, negative 1 is less than or equal to x

is less than or equal to 7, the function is

defined for any x that satisfies this double

inequality right over here. Let’s do a few more. The function f of x is graphed. What is its range? So now, we’re not

thinking about the x’s for which this

function is defined. We’re thinking about

the set of y values. Where do all of the

y values fall into? Well, let’s see. The lowest possible y value

or the lowest possible value of f of x that we get

here looks like it’s 0. The function never goes below 0. So f of x– so 0 is less

than or equal to f of x. It does equal 0 right over

here. f of negative 4 is 0. And then the highest y

value or the highest value that f of x obtains in this

function definition is 8. f of 7 is 8. It never gets above 8, but it

does equal 8 right over here when x is equal to 7. So 0 is less than f of x, which

is less than or equal to 8. So that’s its range. Let’s do a few more. This is kind of fun. The function f of x is graphed. What is its domain? So once again, this function

is defined for negative 2. Negative 2 is less than or

equal to x, which is less than or equal to 5. If you give me an x anywhere

in between negative 2 and 5, I can look at this graph to see

where the function is defined. f of negative 2 is negative 4. f of negative 1 is negative 3. So on and so forth,

and I can even pick the values in

between these integers. So negative 2 is less than or

equal to x, which is less than or equal to 5.

## 12 Comments

## goldensilverstar

Do harder ones like Eulers fiction and natural logs

## lexi gomez

I hate math ._.

## lexi gomez

I hate math ._.

## Anna Fear

Thank you so much!i was struggling with my math hw today and this really helped me understand:).Both of my parents were busy so I'm so thankful I found ur account.:DKeep making ur awesome videos and helping others:).

## Mathematics

Why do only the easy ones?

## Abigail Bui

Thank you! This was very helpful.

## Jessica Smith

what you said below

## tarik

I GET THIS I NEED THE RANGE

AHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHHH

## Reinvention

You described this so well by saying the highest and lowest point. My teacher never even told me that was where you were supposed to get the values from.

## Yan Markos Romero Figueroa

I have a exam of pre calculus tomorrow ðŸ˜¢ðŸ˜”

## justine case

When the teacherâ€™s assistant makes a comment and assumes that the reason you donâ€™t watch these videos, is because she thinks they intimidate you.ðŸ™„ When in reality he stutters and repeats himself and. Instantly for me, itâ€™s like Charlie Brownâ€™s teacher talking.

## EriCosmos Tech

So so clear & easy to understand from anywhere….