Question

5. given no other restrictions, what are the domain and range of the following funtction? f(x)=x^2-2x+2 if your in connexus and have done the algebra 2 final could you give me the awnsers

Answer 1

The range of a function is the set of numbers that you can insert into and will give you a result.

Answer 2

So for example f(x)=1/x doesnt make sense at x=0 because you are dividing by 0. For any other number it will give some kind of result

Answer 3

For your function is there any x that you put in and get nonsense?

Answer 4

idk thats what the question asked and i dont unerstand what to do?

Answer 5

You have to find 2 things: the domain and range

Answer 6

And I have been an idiot sorry :D
So far what I was talking about is the domain

Answer 7

lol its fine can you just help me get the awnser

Answer 8

Sure your function is f(x)=x^2-2x+2
This function makes sense for any x.

Answer 9

This means that the domain of the function is all the real numbers.

Answer 10

For the range of the function you have to find the values that this function can take.

Answer 11

so how do i find the range?

Answer 12

YOu can use the perfect square method.
(x-1)^2=?

Answer 13

Well this method needs some practice.
f(x)=x^2-2x+2
For this method forget about the +2 (the constant) for a moment

Answer 14

Just concentrate on x^2-2x

Answer 15

ok

Answer 16

You can make a full square of the above by writing
x^2-2x=(x-1)^2 -1

Answer 17

Because (x-1)^2 = x^2-2x+1

Answer 18

Is this clear?

Answer 19

no im lost....

Answer 20

haha sorry I have been too quick maybe

Answer 21

no i jut havent done enything like all year so idk like anything so could you maby just give me a free awnser so i can keep going also could u help with some more?

Answer 22

Your goal is to make a graph of this function. Now it is easy to graph quadratic functions that are in the form of lets say (x-5)^2 +12

Answer 23

Well I can give you the answer, it is very easy for me. But what is the point ?

Answer 24

You should try to do it on your own

Answer 25

to help me pass my algebra 2 semester final

Answer 26

cool but for that I will have to pass a test where I am not gonna be helping you

Answer 27

you will :D

Answer 28

OK lets give it another go, shall we?

Answer 29

(a-b)^2=a^2-2ab+b^2
I really hope you know this

Answer 30

no i dont not really

Answer 31

Oh OK this is a problem!

Answer 32

yeah i told you i dont understand any of it

Answer 33

(a+b)^2
(a-b)^2
(a+b)(a-b)

These are very common in maths.

Answer 34

It is a MUST for algebra. You can work these out by expanding the brackets.

Answer 35

(a+b)^2=(a+b)*(a+b)

Answer 36

Do you know how to expand that bracket?

Answer 37

ok yeah

Answer 38

for our problem we need the (a-b)^2
Go quickly expand it and give me your result. I need a toilet break

Answer 39

So (a-b)^2=(a-b)(a-b)=a^2-ab-ba+b^2=a^2-2ab+b^2