Question

14. Express f(x) = |x| as a piecewise function.

a bit confused.

I understand you set parameters in piece wise so.

How do I express this?
x>0 then x is positive

if x<0 then x is positive?

Answer 1

what do you mean by x<0 then x>0?

Answer 2

x<0 does not imply x>0

Answer 3

Yeah I know it doesn't imply it, that's why I was confused.

Answer 4

Let's look at an example
|5|=5 <-- the 5 inside was positive
|-5|=-(-5) <--the -5 inside was negative

Answer 5

So if x is positive then what can you say |x| equals?

Answer 6

I couldn't think of something that showed f(x) = |x|

Answer 7

It equals a positive number

Answer 8

x is a positive number

Answer 9

Just as if it's negative it equals a positive number

Answer 10

so can |x|=x if x>0

Answer 11

just like |5|=5 because 5>0

Answer 12

Yes I believe so

Answer 13

Yes that makes sense

Answer 14

|-5|=-(-5) look at this

Answer 15

the number inside is negative
in order to get a positive out of it we need to multiply inside number by -1

Answer 16

so if x<0 then |x|=?

Answer 17

-1(-x)?

Answer 18

Or just x?

Answer 19

well remember x is negative
so -1(-x) is actually going to be negative

Answer 20

|-5|=-(-5) where -5<0
replace -5 with x

Answer 21

Ah wait so it's |-x|=-(-x) where -x< 0

Answer 22

if i wanted to replace -5 with x
wouldn't it be
|x|=-x when x<0

Answer 23

OHHHH

Answer 24

Wow that just clicked in my head

Answer 25

yeah and if we graphed |x| it looks like