Notes

as b gets larger, the function grows slower.
log base zero is undefined
dese arrrrrrr mah knotes
as b gets closer to zero from 1 the decay slows down.
if were drawing a graph we get something like this
theres also one thing i noticed up here
vertical asymptote
so x equals zero is the vertical asymptote
thers a lot of places where its undefined past zero
so uh, yep
right
befoer you do that i just wanna uh
is this the same for exponentials
which one grows faster, 3 to the x
with exponentials as b gets bigger
asymptote
so logarithms and exponentials
unfreeze
alright, ill zoom in for you 2
our original equation is y=2^x
the blue one
you didnt change the base, change the x or tchange the outside
but keep it 2 to the something
uh you wanna
...
ook so were not doing thw log anymore
so right now we...
have they been sihfted, have they stretched, have they been reflected
good think
whos got it
how to make it not be what?
so you got to try to get that blue one
what do you see for sure between these 2
what kinda transformation d you see
you think dowm, how many
wheres intersection
i dont think it works like that
so wheres this one level out at
so we now we have a shift down of four
minus four
2x-4
so so far we have the uh the vertical shift but it seems to me that this guy is also stretching out a little bit
so what can we do to give it
is it vertical
umm yes
so how de we make it a vertical stretch
well umm, yeah
horizontal shrink
on the inside
wheres the x, this is where the inside of the function is
so if i wanna do a horizontal vertical shrink i wann do
what should we do, what we expect or the opposite
how bout you guys try some bigger numbers out
so you had the right one waht actually makes it four
uh ben, what dd you do
2
we tried out 2
we know that is going to shirkn like this
ummm, so if you graph this so like you can click maybe the 5 point
so i can click on the point on my graph and if you guys have the same point you have the same graph
smack smack
there we go
i could click at the intersection
or we can click at a nwe poi t
aas your x
yes??
firckle frackle thats not right
not literally yeah but actually change something to it
THERE WE GO!
you actually werot e that down, same.. uhhh
nooo
YES?
same
uhh what?
mhmhmh
holy ****
i want hamster
hamster become chew toy
close we also interesect at five pout
no she said lemon juice
coming, good job girls
uhm kida works, its not the right one
ok so, we know that it interesects at the 5 point
flip about y=zero
to the -x
all it does is flip it
at zero five theres an intersection
since this is an intersect
so if i plug it into our equation
whats anything to the zero
one
everyone say it
ALL: anythign to the zero is one
L:how do i make it a five
Nnegative 5
N:woooh
Lthey did -e to the negative x plus 1.61
G: so what hes showing you by plugging in a point
G:the homework and the test will be via multiple choice liek last time
Lno
G: god no
L:log of x plus one
M:mmanamna
L:uh there are

G: so which ones log
M:i do
L: alright which one which
M:blue one
L:ok so
M: oh wait i messed up
L: so this
G: are you sure thats the pint zero one
G:im asking the students
L:oh
G:its alright
A:JIm, JIM
L: if its going to be shifted up one
A: one one
ALL: one one
L: thi one intersects oe one
G:the other thing is, where are the vertical asymptotes
ALL: zero
G:whats goning to change is one zero is going to go toone one
L: alriht, yep
L: ok, if were givin any of these points