Question

please help step by step :)

f(x)={x+2 , if x<0
{1-x , if x>=0

Answer 1

What's the question?

Answer 2

I need to find the domain and sketch the graph of the function.

Answer 3

OK, so the domain is every value of x that we can put into the function. Since f(x) is defined for both x<0 and x>=0, we can see that we can put in any value of x that we want, so the domain will be the real numbers. Do you understand this bit?

Answer 4

so basically the domain will be any real numbers that are <0 or >=0 ?

Answer 5

but its good to write that x belongs to real number

Answer 6

so is it x+2>0 and 1-x>=0

x>-2 and x>=1 ?

Answer 7

no,for domain u see for what values of x, f(x) is defined.
here it is defined for all real values of x.
anything else is not required/correct.

Answer 8

.... I'm confused?

Answer 9

domain is (-infinity,infinity)

Answer 10

how is it though?

Answer 11

because the function is defined for every value of x from -infinity to infinity
as explained already.

Answer 12

with no restrictions on x

Answer 13

oh okay sorry. I had to re-read it all to understand it. and to graph it I just input x+2 and 1-x and press graph on my calculator which creates which is why the domain is (-inf,inf)?

Answer 14

because the lines go on.

Answer 15

yes,if there's a break or discontinuity,then at that value,f(x) will not be defined,and that point will be removed from the domain.

Answer 16

okay thank you!

Answer 17

welcome :)