SOLUTION: what does this look like plotted out on a graph? I want to grasp the knowledge but need to see it in front of me as an example. Thank you for your help. y = |x| + 3

Algebra ->  Graphs -> SOLUTION: what does this look like plotted out on a graph? I want to grasp the knowledge but need to see it in front of me as an example. Thank you for your help. y = |x| + 3      Log On


   

Question 153933: what does this look like plotted out on a graph? I want to grasp the knowledge but need to see it in front of me as an example. Thank you for your help.
y = |x| + 3
Found 3 solutions by stanbon, Fombitz, josmiceli:
Answer by stanbon(75887) About Me  (Show Source):
You can put this solution on YOUR website!
Graph y = |x| + 3
----------------------
graph%28400%2C300%2C-10%2C10%2C-10%2C15%2Cabs%28x%29%2B3%29
Cheers,
Stan H.

Answer by Fombitz(32388) About Me  (Show Source):
You can put this solution on YOUR website!
Remember
system%28abs%28x%29=x+%28if+x%3E0%29%2Cabs%28x%29=-x+%28if+x%3C0%29%29
Let's plot it.
Let's go from x=-5 to 5 in steps of 1.
y%28-5%29=abs%28-5%29%2B3=5%2B3=8
y%28-4%29=abs%28-4%29%2B3=4%2B3=7
y%28-3%29=abs%28-3%29%2B3=3%2B3=6
y%28-2%29=abs%28-2%29%2B3=2%2B3=5
y%28-1%29=abs%28-1%29%2B3=1%2B3=4
.
.
.
y%280%29=abs%280%29%2B3=0%2B3=3
.
.
.
y%281%29=abs%281%29%2B3=1%2B3=4
y%282%29=abs%282%29%2B3=2%2B3=5
y%283%29=abs%283%29%2B3=2%2B3=6
y%284%29=abs%284%29%2B3=2%2B3=7
y%285%29=abs%285%29%2B3=2%2B3=8
.
.
.
The graph shows the V shape characteristic of absolute value functions.

Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
Actually, the best way to understand it is not by staring
at a graph (you can do that later). The best way is just
to reason out what it should look like.
I'll do it in steps:
(1) The right side (therefore y) can never be negative
because neither of the two terms on the right can ever be negative.
abs%28x%29 means "make the sign of x positive,
no matter what x is.
--------------------------
(2) The right side can be equal to 3, but it can never
be less that 3, since abs%28x%29 will never subtract
anything from it
--------------------------
(3) I can get rid of the absolute value sign if I replace
the equation with 2 equations like this:
When x is zero or negative the equation is
y+=+-x+%2B+3
When x is zero or positive the equation is
y+=+x+%2B+3
Suppose x+=+-5, then
y+=+-%28-5%29+%2B+3
y+=+8
This shows that y is positive for +x
and -x
----------------------------
(4) Using the reasoning of these steps, y+%3E=+3
x can be any value (there are no restrictions on
what you make it).
(5) To draw the graph, draw y+=+-x+%2B+3, but don't let
the line go below y+=+3, then draw y+=+x+%2B+3
and don't let the line go below y+=+3
----------------------------
Hope that's not too confusing. There no easy way except to
apply a step-by-step reasoning that makes sense to you.