Question

Identify this function as continuous or not continuous on (-infinity,infinity):

y=lxl-4

Answer 1

any ideas?

Answer 2

I have the answer and it is continuous but im not sure how to get that...like how do you know it is continuous?

Answer 3

well

|x| = x if x >=0

or

|x| = -x if x <0


so effectively, y = |x|-4 is made of the two equations

y = x - 4 if x >= 0
y = -x-4 if x < 0

and they together form y = |x|-4

Answer 4

since y = x-4 and y = -x - 4 are both continuous at any point on either line, this means that y = |x|-4 is continuous everywhere

Answer 5

ohh that makes sense thank you!

Answer 6

you're welcome