Question

how do you find the domain and range of:
f(x)= 1/2|x-2|

Answer 1

Domain = all values of x you can substitute into the equation such that you don't have:

1) Log of a number <= 0
2) Square root of a negative number
3) 1 / 0

Range = All values of y the function reaches when you input all the values of x it can take on.

Answer 2

I thought it would be (-infinity, 0), things like that

Answer 3

is this the equation?
\[\frac{1}{2|x-2|}\]

Answer 4

no

Answer 5

it's the way I posted it

Answer 6

:) the way you posted it can be interpreted a number of different ways

Answer 7

\[\frac{1}{2}|x-2|\]
if this is it you should have posted it like this:

(1/2) |x-2|

Answer 8

I was told by my teacher that the domain is from (-infinity,infinity) I don't even know the range. I'm so lost as to why they gt these as answers. Especially since the grapgh of an | | equation looks like this

Answer 9

the range is the lowest value up to the highest value

Answer 10

Yes, the equation is: 1/2 times the absolute valuse ||, of x-2- |x-2|

Answer 11

and that is not the graph of what you have posted; your equation has a horizontal shift, not a vertical shift

Answer 12

I know, I was just saying that an absolute value graph looks like that

Answer 13

The domain of |x| is all values of x. The RANGE of |x| is all values of x greater than or equal to zero. (obviously, you can't get a negative y-value by taking the absolute value of x.

1/2|x| is just "stretching" the graph, domain and range remain unchanged.

1/2|x-2| is shifting the vertex two units to the right. (Because x = 2 gives y = 0 ). The domain and range remain unchanged.

Domain = all real numbers
Range = all real numbers GREATER THAN OR EQUAL TO zero. :)

Answer 14

that would be one drawing yes :)

But the equation you have just moves side to side; so the range is unaffected; it remains (0,inf)

Answer 15

The blue function is 1/(2|x-2|), which has an asymptote at x = 2 and the domain is all real numbers EXCEPT x = 2.

Answer 16

thats pretty teacher

Answer 17

Thanks, I made it in geogebra, I'm giving a demo of it now if you or anyone else is interested. :)

Answer 18

Okay, so based on your gorgeous graph, here are my questions.

Answer 19

Wouldn't one of the domins be: (-infinity,0)

Answer 20

An another (0,2)

Answer 21

when you find the domain look from left to right
the domain is where the function exist

Answer 22

is there any real input that you can think of that would not give you a real output?

Answer 23

well I know that it'd an infinite graph

Answer 24

the domain is all real numbers because for each of these real numbers there is a real output
(-inf,inf)=the set of all real numbers

Answer 25

if we had 1/(2|x-2|), the domain would be all real numbers except x=2 since that would give us zero on the bottom

Answer 26

Myininaya -- great explanations. :)

Answer 27

thanks :)