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Mathematics 21 Online
Nicole:

http://prntscr.com/nl3kaa

Nicole:

@Vocaloid @Narad

Nicole:

?

Nicole:

@Hero

Narad:

Question 1 A direct proportion doent have reciprocal, squares or square roots

Narad:

Question 2 y=a/x with the values given y=5 and x =-1, you can calculate a, then obtain the equation

Narad:

Question 1 is not correct

Narad:

Question 2 is not correct

Narad:

Question 3 in not correct

Nicole:

so question 1 b?

Narad:

yes, this is correct

Nicole:

for number 2 a=-5

Nicole:

so A?

Narad:

Yes

Nicole:

and 3 is D?

Narad:

Yes

Nicole:

http://prntscr.com/nl3tan

Narad:

No

Nicole:

isnt it 6*3? or 6/3?

Narad:

The same as you did before in 2 and 3

Nicole:

D?

Narad:

yes

Nicole:

http://prntscr.com/nl3uun

Narad:

A direct variation is a straight line

Nicole:

So its inverse

Narad:

yes

Nicole:

http://prntscr.com/nl3wqs ignore my answers^

Narad:

A direct proportion is y=ax Sustitute the values to find a

Nicole:

so y=a/-3 ?

Narad:

Sustutute the values y=15 and x =-3, to find a

Nicole:

15=a/-3

Narad:

y=ax a=y/x

Nicole:

a=-45

Narad:

no you are multiplying

Nicole:

Can you make this clear please because im plugging in the numbers and I get -45

Narad:

y=ax a=y/x=15/(-3)

Nicole:

Now im getting -5 where do I put the 6 in this

Narad:

y=-5x Now, plug in x=6

Nicole:

-30

Narad:

yes

Nicole:

so for the next question a=6/-1 is -6 y=-6x x=5 is -30

Nicole:

so B?

Narad:

yes

Nicole:

okay http://prntscr.com/nl46xj

Narad:

y=1/x y=1/x-4 -4 moves down

Nicole:

so A

Nicole:

since down

Narad:

yes

Nicole:

http://prntscr.com/nl4aea

Narad:

The parent function is g(x)=1/x and f(x)=1/(x-6)+7 There are 2 transformations The +7 will translate up by 7 units and the -6 will translate 6 units to the right

Nicole:

okay http://prntscr.com/nl4f9e

Narad:

The parent function is g(x)=1/x f(x)=a/(x+h)+k a is a vertical stretch h is a horizontal shift (a>0, to the left), and (a<0, to the right) k is a vertical shift, k>0 to the top and k<0 down

Nicole:

Got it http://prntscr.com/nl4fx0

Narad:

It's the same the last question except that a=1

Nicole:

but this is range

Nicole:

f(x) < -4 ?

Narad:

The domain is \[\mathbb{R} -(-1)\] y=3/(x+1)-4 y+4=1/(x+1) x+1=1/(y+4) x=1/(y+4)-1 So the range is \[\mathbb{R}-(-4)\]

Nicole:

Ohh okay http://prntscr.com/nl4pgh

Narad:

Let \[y=2/(x-3)-5\] Can you find x in terms of y?

Nicole:

how can I do that

Nicole:

-5?

Narad:

yes \[y \neq -5\]

Nicole:

okay http://prntscr.com/nl4q5s

Narad:

I think it's a litle smaller than -0.5

Nicole:

0.75?

Nicole:

or negative

Narad:

-0.75

Nicole:

okay http://prntscr.com/nl4sdb

Narad:

Your answer is correct, if you plug in the value of n=1/2, you'll see that RHS is not equal to LHS

Nicole:

okay http://prntscr.com/nl4t1u

Narad:

The same as before y=a/x

Nicole:

2=a/9 a=18

Narad:

yes

Nicole:

but dont I have to write an equation?

Narad:

yes y=a/x

Nicole:

http://prntscr.com/nl4x0a 5=a/3 a=15

Narad:

and y=15/x

Nicole:

got it http://prntscr.com/nl4xxa

Nicole:

direct?

Narad:

yes

Nicole:

http://prntscr.com/nl4y4x

Narad:

The same as before y=ax

Nicole:

15=a/-3

Nicole:

-45

Narad:

no

Nicole:

then what is it?

Nicole:

this is timed please

Narad:

y=-5x=-5*4=-20

Nicole:

so -20 is the answer?

Narad:

yes

Nicole:

http://prntscr.com/nl53ke

Narad:

What would you say?

Nicole:

im not sure tbh

Narad:

at x=1, what's the value of y?

Nicole:

-1?

Narad:

> -1

Nicole:

oh so thats the answer?

Narad:

no, it's between 0 and -1

Nicole:

how do I know which one

Narad:

you see where is x=1 you go vertically down until you meet the red curve

Nicole:

isnt it -4 then?

Narad:

Yes

Nicole:

okay

Nicole:

http://prntscr.com/nl59lr

Narad:

The same as the last question

Nicole:

-3?

Narad:

-0.3

Nicole:

oh okay http://prntscr.com/nl5ao6

Narad:

The same as before

Nicole:

how do I do the transformations again?

Narad:

\[f(x)=a/(x+h)+k\] a=stretch vertically h=horizontal shift, a>0 to the left, a<0 to the right k=vertical shift, a>0 to the top, a<0 down

Narad:

h>0 to the left, h<0 to the right k>0 to the top, k<0 down

Nicole:

can you plug in the numbers please

Narad:

Stretch vertically 5 times +1 is a horizontal shift to the left -7 is vertical shift of 7 units down

Nicole:

okay http://prntscr.com/nl5b2l

Narad:

Graph moves 10 units down

Narad:

Graph moves 5 units up

Nicole:

http://prntscr.com/nl5fus

Narad:

\[y=-6/x\] y=-6/-1=6

Nicole:

http://prntscr.com/nl5hol

Narad:

Already done, this is false

Nicole:

http://prntscr.com/nl5iaw

Narad:

already done

Nicole:

but the numbers arent plugged in?

Narad:

Stretch vertically by a factor of 3 Horizontal shift to the left by 2 units Vertical shift up by 4 units

Nicole:

okay thank you

Narad:

ok

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