Question

How would you write the absolute value of x as a piecewise function?

Answer 1

That would depend on the piecewise function. Present the function AND your best efforts.

Answer 2

Okay! The way it's been written on this packet is literally - Write the absolute value of x as a piecewise function.

Answer 3

First answer the following:
|2|=?
|-2|=?
|0|=?

Answer 4

|2|= 2
|-2|= 2
|0|= 0

Answer 5

@freckles ^

Answer 6

cool

Answer 7

notice the input and the output are the same for the first one
notice the input and output are different for the second one

Answer 8

Okay!

Answer 9

so
|x|=x if x is?
and
|x|=-x if x is?

Answer 10

things remained unchanged if the input was ?

Answer 11

Positive?

Answer 12

right
so |x|=x if x is positive right?

Answer 13

the input and output are opposites if the input was ?

Answer 14

Negative?

Answer 15

right

Answer 16

|x|=x if x is positive
|x|=-x if x is negative
|x|=0 if x is zero

Answer 17

The absolute value function is indeed a piecewise function; the graph is made up of two lines that intersect at the origin. Please graph it.

You must specify an INTERVAL describing the x values for which the absolute value function is the same as y1=-x and another INTERVAL

Answer 18

...describing where the abs. val. function is y2=+1x.

Answer 19

In other words, write out two sets separated by a " U " (for Union).

Answer 20

Oooo I'm lost now.

Answer 21

This is NOT the answer, but is an illustration of what I mean:

(-inf, -5) U (-5, +inf)

OR

-inf < x < -5 U x > -5

Answer 22

I know the U (union) set up. But I'm not sure how to go about what you're saying. Would the answer be in that format?

Answer 23

"write the absolute value of x as a piecewise function"

That absolute value function is defined as |x|.
To the left of zero, this boils down to (is equivalent to) -x.
To the right of zero, ... +x.

Your job is to identify the domain as a set; that domain will be the UNION (U) of two different sets.

Answer 24

Again, I urge you to graph y=|x|.
You will see immediately where the equivalent graph is y=-x and where it is y=x.

Your task is to specify WHERE (for which x) the graph is equivalent to y=-x and WHERE to y=+x.

Answer 25

Well, I graphed it and then looked at the table. The values are showing as (-1,1) (0,0) (1,1) and following that pattern from there on out.

Answer 26

Your answer must take on one of the two following formats:

(-inf, -5) U (-5, +inf)

OR

-inf < x < -5 U x > -5

... and you must, of course, replace the example -5 with another value suitable to y=|x).

Answer 27

|x|=x if x is positive
|x|=-x if x is negative
|x|=0 if x is zero

@ontour He is wanting you to translate our if parts into math symbols

Answer 28

you could combine two of those into one
and just have two pieces instead of three

Answer 29

How would this be combined? I'm not sure how to go about it

Answer 30

just look at this part first:
|x|=x if x is positive
|x|=-x if x is negative
|x|=0 if x is zero
and write in math symbols

x is positive <--how do you write this as an inequality?
x is negative <--- how do you write this as an inequality?

Answer 31

0 is the only neutral number
what do you know about numbers GREATER THAN zero?

Answer 32

They're positive!

Answer 33

right so x is positive ... means x blank 0

Answer 34

what is the blank

Answer 35

what symbol

Answer 36

Greater than!

Answer 37

>
which is this symbol right?

Answer 38

@freckles: Nice work.
Could you create a simple, piecewise linear function, graph it and explain how we specify the domain as a collegtion of domains joined by " U "? Thank you.

Answer 39

Yes! So x > 0

Answer 40

So X > 0, X < 0, X = 0

Answer 41

right but tag the piece you are referring to for each inequality
so |x|=x if ___
and |x|=-x if ____
and |x|=0 if _____

Answer 42

Got it!

|x|=x if X >0
and |x|=-x if X < 0
and |x|=0 if X = 0