hi everyone mahmoud is here today i will
show you really important pro tips about
desmos art
remember the pikachu graph we created
together in video 3.
today we will graph it again and color
it and we will do it professionally
let's get started
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this is the fifth video of desmos art
video series in the first four videos i
talked about basics
and now let's make things a little bit
more professional
and let's start working here is the
pikachu graph
if we color it by using the techniques i
showed you in video 3
this happens colors overlapping their
parts look like uncolored even though
they colored them
so the methods in video 3 works great
between the lines
and in circles but not in curves so we
need to do a
more professional way of coloring
actually we need to graph it again
and i will show you how you can combine
several functions
first of all if x values or viables are
not overlapping
use piecewise functions to combine
things um for example
the right side of pikachu you see y
values are not overlapping right
all three parts have different white
values so we can combine them
by using piecewise functions by creating
y
intervals let's name the piecewise
function
if you want to give a letter name only a
letter name like a
just type and put equal sign but if you
want to
name it as a word let's say side
write the first letter then other
letters needs to be
written as subscripts so press shift
and dash it goes to underscore and you
continue writing
other letters after that go one unit
right and put equal sign
open the curly brackets and write the
functions
i will start with the first one remember
we write the interval first
put column and write the function we
created all these functions in video 2
so i am using the same now put comma
write the second interval column and the
function great
okay when we check the third function we
realize that it is written differently
because the interval is for variable x
not for y
we cannot directly include it in this
piecewise function
because the variables are different
right but we can use the inverse
function
so i will go to symbolab.com a super
useful website
and find the inverse of this because
it's a square root function
it's going to give me two answers and
one of them will work
let's try this one
and of course we need to swap x and y
values and yes
it is the correct one great we also need
to write the interval with y values
and let's include this one to piecewise
function
great now you see guys i used a
piecewise function to combine
three functions i will do the same for
other parts
let's continue to do it for the top
three functions here
all of them has x intervals so no
problems let's combine them
done by the way i know we can use
absolute value for the top
but i will talk about that in a few
minutes for the bottom
no need to combine anything because it's
just one function let's name it
okay and the left side
we don't actually need to graph this um
because absolute value of x
on the right side will give us the left
side but if you want to graph it use the
same methods we use
for the right side i am graphing it
right now but i will erase it
and use the absolute value
now we got the head by only using four
functions
i will change the inequalities because
it will be important to understand the
next part
um okay here are my functions and now i
will combine these four
in only and only one expression since
the values are overlapping
we cannot use a piecewise function
anymore there's another way
using maximum and minimum we use maximum
and minimum in three different ways
first to combine functions second to
color them
and third to choose specific part of the
graph i will show you all three
and i will start with the first one
let's start with combining these
four functions to do that type 0 and
equal sign
and then type maximum max just max
open the brackets now we need to decide
what functions to choose
because i will use the same expression
to graph as well
i will choose the top part like y minus
tau
so it will choose the top curve and when
we graph it it will choose
below the top part let's continue put
comma
then write the next part for the bottom
same logic
but we go with bottom minus y let's see
what happens
yep you see guys it combined the
intersection of these two functions
maximum chooses the intersection and
minimum
shows us the union that's why i'm using
maximum here let's add the sides
i will add the right side first so the
left part will be x minus
right side and i told you right we don't
need to graph the left side because
it is symmetric so i can just use the
absolute value sign here
and boom it chooses both of the sides
let's hide all these functions
wonderful now i combine everything let's
make it black
great now it's time to talk about
coloring so when i change the equal sign
with an inequality
it starts coloring for example smaller
than
colors outside and bigger than colors
inside
again maximum basically graphs the
intersection and minimum graphs the
union okay
i will also combine other functions
let's combine both pupils
i will just choose one of them move
everything on one side um the left side
will be zero and because it is symmetric
i will use the absolute value of x
and boom let's name it purples
and when you do that the circles
disappear but don't worry we can use it
and we have circles for the eyes and the
blushes we're going to use the same
method this is how vigorous absolute
value now let's clear the face
i will copy and paste this one first i
will change the equal sign and write an
inequality here
and now we are going to exclude eyes and
blushes
from this area to do that just add the
function like that
minus eyes comma minus plush
and that's it to avoid those dashed
lines
go to settings and disable lines okay
let's talk about the nose and the mouth
these are the equations we used for the
nose
since both x and y values are
overlapping i cannot use a piecewise
function
let's say i have these two equations
write the first equation like that
0 equals y minus 2. then subtract the
second one
i am using it like that because i will
use this part
divide this part by two write all in
absolute value
write x in absolute value as well i will
put another brackets for you to see
things clearly
then choose all this part without y
paste outside the absolute value and
only only change the sign
boom it gives you a triangle
here how we combine two equations to get
a symmetric shape
not just a triangle we can get different
shapes now i will use the numbers
in the original function
and yes we get the nose um let me paste
it here
and name it i will also exclude
this area here from the face great and
we will use the same method
for the mouse let's take the functions
is symmetric so
um these two enough move everything on
one side
left side is zero add the other function
divide this part by two
make x and absolute value and add
absolute value for all the part
copy and paste this part outside
change the sign boom great let's paste
it here
and name it as a mouth
subtract the area wonderful let's color
it
um the original yellow the pikachu
yellow by the way to add the original
color guys
i used the method i showed you in video
three and finally
i will fix the ears and to do that we
will use the maximum and minimum again
let me show you how it works let's say
here's the function
if you choose the minimum until 2 it
graphs it like that
and you see y is less than 2
and 2. if you choose the maximum it does
the opposite
let's have a parabola
and yes it works the same and here is
our function i will remove the interval
and get the maximum let's say two
yeah i will name it as ear so look at
this changing the constant volume here
changes the graph like that
great let's copy and paste it to pikachu
graph
okay i need to change the constant value
and i think 2.9 is good
so it doesn't cross the graph it's not
really disturbing
it is a straight line and curvy on the
ear
only this is the last way of using
maximum and minimum
now i will also exclude the ear parts
from the yellow area
we're going to add x minus here here and
when you write x in absolute value
you can clearly see that both sides are
excluded from the yellow area
and this is great okay we are done with
the yellow part
it is time to color other parts let's
start with the ears
um these parts will be black i will use
maximum again to color and the area i
want to color is between the ear
right side and the top function so i
will go with 0 is bigger than maximum
x minus right side x in absolute value
because we also have the left side
symmetric right and y minus top and er
minus
x and x in absolute value again great
i'll make it bigger than equal to to
color the curve between the areas
the area between the eyes and the pupils
will be black
so two functions i had another maximum
here eyes
comma minus pupils for nose the same
idea but it's
just one function actually you don't
need to use the maximum here
it is the same for blush as well um you
don't need maximum
it's a standard color because we only
have one function
for the mouth we need another curve
because if you graph it it will look
like that
so it's not how pikachu looks like right
let's go back to the original function
and copy and paste the curve we have
here it is let's name it as tong
we don't need to domain by the way let's
change the area
and add y minus tong here great and
for the remaining part we can add a
black area the same idea
finally i will copy and paste this curve
to complete my graph
done i think we did a great job you see
the difference between both graphing
methods
on the left i use inequalities like in
video 3
on the right i used maximum um you see
the graph on the right looks
much much better and also on the left we
have
60 entries but on the right it's only
20. by the way the links for the
original pikachu and the colorful one
both in the description below
okay i hope you liked the video and if
you want to help me create more videos
like this one
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i will answer your questions as early as
possible see you next time
keep watching mathematics goodbye
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you