Math help (2 Viewers)

[Fawun]

Re: Math help (Because Carrot made me do this)

It should also have a negative sign, but when you simplify (-x)², it goes back to x².

I know that but read my previous post please.

 

[RivalryofTroll]

Re: Math help (Because Carrot made me do this)

Also, for my example, what do I do next? How do I know whether it's an odd or an even function? Do I like factorise it or something?

You know it's f(-x) = f(x) for even and f(-x) = -f(x) for odd and none of those for neither.

If it's clearly not an even, you'll check whether if it's an odd by taking the negative out.

E.g. -x^2 - 1 becomes -(x^2 + 1)

and you can tell whether that is equal to -f(x) or not.

If it's not then it's neither.

 

[D94]

Re: Math help (Because Carrot made me do this)

Generally,

(negative value)^{even number} = even value

e.g. (-x)⁴ = x⁴

i.e. (-2)⁴ = 16

(negative value)^{odd number} = odd value

e.g. (-x)³ = -(x³) = -x³

i.e. (-2)³ = -8

NOTE: (-x⁴) =/= (-x)⁴

Also, for my example, what do I do next? How do I know whether it's an odd or an even function? Do I like factorise it or something?

If you see your result for f(-x) is now equal to the original function, f(x), then it is even. You just say something like "f(-x) = f(x) therefore the function is even".

If you see your result for f(-x) is now equal to -f(x) i.e. -1 * f(x), f(x) is odd. Likewise, you say something similar to "f(-x) = -f(x) therefore the function is odd".

Else/otherwise, you just say it is "neither even nor odd".

If the function returns back to f(x), then you don't need to factorise anything - you just say it's even. If you see a negative sign, then factorise the negative sign out (-1), i.e. -x-2 = -(x+2), then look inside the bracket to see if that expression equals the original function. If it does, then it's odd, otherwise, it's neither.

 

[Carrotsticks]

Re: Math help (Because Carrot made me do this)

Fawun, I think you really should revise your algebra and the idea of a function, before trying to tackle odd/even functions.

 

[twinklegal19]

Re: Math help (Because Carrot made me do this)

Fawun, I think you really should revise your algebra and the idea of a function, before trying to tackle odd/even functions.

+1

Everything will make so much more sense, trust me

 

[Fawun]

Re: Math help (Because Carrot made me do this)

How do you sketch square root graphs? Like I know that for example



You just like sub in y=0 and x=0 to find the intercepts if there are any y/n?

So how I would do it is:


when x=0, y=1
when y=0, x=-1

and so your graph should look like this:

right?

Well how would you do it for this question?



Thanks guys

 

[deswa1]

Re: Math help (Because Carrot made me do this)

Well how would you do it for this question?



Thanks guys

Personally, I would recognise that x is between -1 and 1 (as otherwise the function is not defined). Then I would (probs not the best mathematical way), sub in the points x=1, x=0, x=-1 and a few other points and connect the dots. A better way (that would take more time) would be to graph the two functions seperately (i.e. y=root (x+1) and y= root (1-x)) and then add ordinates

 

[Fawun]

Re: Math help (Because Carrot made me do this)

Personally, I would recognise that x is between -1 and 1 (as otherwise the function is not defined). Then I would (probs not the best mathematical way), sub in the points x=1, x=0, x=-1 and a few other points and connect the dots. A better way (that would take more time) would be to graph the two functions seperately (i.e. y=root (x+1) and y= root (1-x)) and then add ordinates

Okay let me just break this down so I understand everything:

Personally, I would recognise that x is between -1 and 1

Where did you get the -1 from? I understand that you got the 1 from the first square root right? but the second square root is a 1 as well.

sub in the points x=1, x=0, x=-1 and a few other points and connect the dots.

Do you just choose random numbers like 1, 0 and -1? Can they be random numbers? and why x=1, x=0 and x=-1? Why can't you do y=1, etc.

A better way (that would take more time) would be to graph the two functions seperately (i.e. y=root (x+1) and y= root (1-x)) and then add ordinates

What is adding ordinates and how do you do that?

 

[deswa1]

Re: Math help (Because Carrot made me do this)

Will answer each question in bold:

Okay let me just break this down so I understand everything:
Where did you get the -1 from? I understand that you got the 1 from the first square root right? but the second square root is a 1 as well.

The minus one comes from the first root. In the second, x has to be smaller than 1 otherwise 1-x is less than zero which is impossible. In the first one, 1+x has to be bigger than 0, so x has to be bigger than -1. So we know that x has to be bigger than -1 but smaller than 1- hence the domain

Do you just choose random numbers like 1, 0 and -1? Can they be random numbers? and why x=1, x=0 and x=-1? Why can't you do y=1, etc.

Not really random no. 0 is always the easiet to test so always do that one. I picked 1 and -1 because they are the endpoints of the domain and its important to see where the curve starts and finishes. Then pick random points in the middle so you are satisfied that you know the path of the curve

What is adding ordinates and how do you do that?

Adding ordinates is basically where you add together the y values for two curves. For example, consider y=x+x^2. This is the same as adding EVERY y value of y=x to y=x^2. Consider for example x=2. y=x gives a y value of 2. y=x^2 gives a y value of 4. Therefore y=x+x^2 has a y value of (2+4=6) at x=2. Do this for all values. So to do it for this question, you graph the two roots and then add their y values

.

 

[Shadowdude]

Re: Math help (Because Carrot made me do this)

Graphs is best taught in person because it's quite graphical.

no pun intended

 

[Fawun]

Re: Math help (Because Carrot made me do this)

Will answer each question in bold:



.

1. For the end points of the domain thingy, do you have to do it for every question? or is it just this specific question?
2. When you sub in numbers like "when x=0, y= blah blah" do you have to do "when y=0?" or can you just do x?
3. Idgi the adding ordinates part still -_-

 

[OzKo]

Re: Math help (Because Carrot made me do this)

1. For the end points of the domain thingy, do you have to do it for every question? or is it just this specific question?
2. When you sub in numbers like "when x=0, y= blah blah" do you have to do "when y=0?" or can you just do x?
3. Idgi the adding ordinates part still -_-

1) Considering that a given x value could result in an undefined y, it is relevant in this case.
2) Don't need to do y=0.

 

[Parvee]

Re: Math help (Because Carrot made me do this)

lol I remember this saying my yr10 teacher told us when we had no clue on how to graph something: "when in doubt, use table of values".

 

[OzKo]

Re: Math help (Because Carrot made me do this)

lol I remember this saying my yr10 teacher told us when we had no clue on how to graph something: "when in doubt, use table of values".

Did this teacher teach Year 11/12?

 

[deswa1]

Re: Math help (Because Carrot made me do this)

What's wrong with table of values? I use it a lot and I do 4U lol

 

[enoilgam]

Re: Math help (Because Carrot made me do this)

lol I remember this saying my yr10 teacher told us when we had no clue on how to graph something: "when in doubt, use table of values".

I used to do this as well as a last resort - pretty fool-proof at times I reckon.

 

[Parvee]

Re: Math help (Because Carrot made me do this)

Did this teacher teach Year 11/12?

Nah he left after we had him for year 10
It was mainly for people who got stuck and had no idea on what to do

 

[OzKo]

Re: Math help (Because Carrot made me do this)

Nah he left after we had him for year 10
It was mainly for people who got stuck and had no idea on what to do

I did this too but I'm wondering if there are any other tricks.

 

[Shadowdude]

Re: Math help (Because Carrot made me do this)

The thing with the table of values is that you'll probably use "plus/minus infinity", -5, -4, ... , 5 or something

This doesn't work if you have a turning point or stationary point at x = 6 or x = 5.00000000000001 even. Or what if x = 2 and x = 3 have the same value but there's a maximum/minimum at x = 2.5?


So really... when you're graphing, you just have to know the shapes of the basic graphs. But, iirc, this is year 10 - they can't make you draw super complex stuff anyway.

But for HSC/Prelim curve sketching, you should have a better toolkit - including knowing shapes of basic graphs, addition/subtraction/multiplication/division of ordinates, knowledge of limits and asymptotes, stationary points, etc.

 

[Fawun]

Re: Math help (Because Carrot made me do this)

All the people in my class say that table of values is a noob way and that it is a waste of time :s

But how would you do this question?



What does the 1 in front of the square root do?

Like when I say

"When x=0, y= 1 - square root 2" right?
and then "When y=0, x=-1"

so those are the intercepts.

How come the answer shows that it goes through the origin? :s