Math Help for AIMS Exam: Formulas, Functions, and Graphs Explained

[QuantumTheory]

Hi, I need some study help for an AIMs test coming up soon. I go to a charter school, a soon where the teachers don't nessicarly have to be qualified to teach. I have 1 teacher. So when most people need help with their math problems, they don't have anyone to turn to except otehr student tutors, I'm one of the tutors.

I have forgot ALOT of formulas and basic math. You see, when I was in 9th grade I was only in pre algebra. When I was in 10th grade I took algebra, but was withdraw and put into a charter school. I finished algebra there, took part of geometry, then that's it, I was done with my credits

I offered to take math again, for more help. I couldn't get it because the teacher was too busy and couldn't help me

So I haven't done math in awhile. Now I'm in a different school and Ic ant take math because I've done all my credits. now the math aims is coming up and I have to pass it!

Remember, I only took some geometry, and then i was done. I never was introduced to quadratic equations, mirror graphs, very basic functions, that's it.

Last time I took the AIMS I just randomly put in bubbles because I just didnt know the answers; I hadnt taken the material before. I am very good in math however, A student

I need help with a function, f(x).

I understand that f(x) is indepdenat, and that x is dependant of the funtion f.
and that x varies with f.

thats about all i know about functions. that and when you insert a number in the x position the function changes.

i heard f(x) is just like y, where y = mx + b

i also need help with mirror graphs of a function

I don't have a specific problem however, i just need a general idea

I just went through my study guide.

It has some good stuff, basic, probability, etc.

WIll i never need FOIL?
i am not good at factoring but i can do it with practice

i know calculus but i can't do it because i don't know factoring well enough

thanks

 

[kreil]

I need help with a function, f(x).

Functions take an input (x) and perform an operation to it to produce the output, f(x). To show that the function is performing the operation on x, it is often written f(x). When you plot a function, this output obtained by performing the functional operation f on x is the y-value on the graph,
so f(x)=y. The points on the graph are thus (x,y) or (x, f(x)). When you are plugging in numbers to get function (or y) values, you simply put in the number in every spot you see an x in the function.

i also need help with mirror graphs of a function

This quick exercise will show you how to move points around on a graph.

1) Plot the point (4,5)
2) If you reflect in the y axis, what is the new point value?
3) If you then reflect in the x axis, what is the new point value?
4) Reflect it in the origin, what are the coordinates now?
5) Finally, reflect in the line y=x


Answers:
2) (-4,5)
3) (-4,-5)
4) (4,5)
5) (5,4)

have you noticed any patterns?

2) Whenever you reflect a point (x,y) over the y-axis the new
point will be (-x,y)

3) Reflection over the x axis: (x,y) --> (x,-y)

4) Reflection through the origin: (x,y) --> (-x,-y)

5)Reflection over the line y=x: (x,y) --> (y,x) (No, I didn't list them backwards, it just refers to the first x,y values)

As for factoring, it can almost always be reduced to a small word problem:

1 $$f(x)=x^2-4x+4$$

"What two numbers multiply to 4, and add to -4?"
The answer is -2 and -2:
$$f(x)=x^2-4x+4=(x-2)(x-2)=(x-2)^2$$


2 $$f(x)=x^2-5x+6$$

"What two numbers multiply to 6 and add to -5?"
The answer is -3 and -2:
$$f(x)=x^2-5x+6=(x-3)(x-2)$$

3 $$f(x)=x^2+8x+7$$

"What 2 numbers multiply to 7 and add to 8?"
The answer is 7 and 1:
$$f(x)=x^2+8x+7=(x+7)(x+1)$$


I hope I helped, let me know if you need clarifications/more help!

~Josh

 

[QuantumTheory]

Thanks Josh. I don't understand what you mean by 'add to -5'

see my problem is this with factoring
On the first one, where does the -4x go?
On each one it appears that the coeffiecent is missing.
I have forgot a lot about graphing. Including x=y.
It is a shame. I shouldve gone to another school which would teach me math with a math teacher.

Im sorry I do not understand the mirror thing. On a lot of things I cannot learn by reading it, I need it hands on. But please continue to try and explain

 

[QuantumTheory]

$$f(x)=x^2-4x+4$$

Ok let me try and do this one..

(x - 4x + 2)(x + 1 + 2)

thats what i get..

Does the coeficent cancel out?

 

[Moo Of Doom]

$$f(x)=x^2-4x+4$$

Ok let me try and do this one..

(x - 4x + 2)(x + 1 + 2)

thats what i get..

Not quite...

Look at your first factor (x - 4x +2). What's x - 4x? And in the second factor, what's 1 + 2? What's wrong here?

 

[QuantumTheory]

Not quite...

Look at your first factor (x - 4x +2). What's x - 4x? And in the second factor, what's 1 + 2? What's wrong here?

I don't know. But I think i was doing the distributive property wrong with factoring. When I was told to distrubite like this before:
2(x + 1) = 2x + 2
But apparently the factor distirubte property is different when you have it like this (x +2)(x -2 ) which equals x^2 + 2x - 2x - 4 which equals x^2 + 0 - 4 which equals x^2 - 4

 

[QuantumTheory]

Now give me a limit problem!

:P

 

[QuantumTheory]

Ok, I found out there is more than one type of factoring, great. I think the one you showed me is difference of squares. But there's other harder ones too! How many methods are there?

Also, how do I do this problem? I can't seem to solve it
16y^2 - 9 in difference of squares

 

[Jameson]

What if you look at it like this: $$16y^2-9=4^2y^2-3^2$$?

 

[QuantumTheory]

What if you look at it like this: $$16y^2-9=4^2y^2-3^2$$?

It's still confusing! I just found out how to factor barely with my teacher who knew factoring. Someone before this posted on how to do it with word problems. I can't seem to do this one as a word problem

 

[Moo Of Doom]

It's still confusing! I just found out how to factor barely with my teacher who knew factoring. Someone before this posted on how to do it with word problems. I can't seem to do this one as a word problem

Think of 4x^2 - 9 as 4x^2 + 0x - 9.

What two numbers add up to 0 and multiply to -9?

 

[QuantumTheory]

Those word problems are hard..

-3 and 3?

 

[QuantumTheory]

anyone know?