Pre-Calculus: Functions

[Graham]

Calculus: Functions
High School level math is required for this guide.

To really jump into functions there is some primary information which you will be aware of. This guide will show people how to solve basic functions and some information about them. There is a multitude of important terms and structures, but this is the surface and should give you a decent understanding. Were going to start simply with the number line, example depicted below.

The Number Line

• The number line is a line which represents (graphically) numbers, both positive and negative, as infinitive number. Points and specific integers can be marked off on the graph, otherwise plotted. Each point is described as it's distance from 0 - the middle on the number line.

Basic Library of Functions
These are basic "facts" from the library of functions, which are always standard and never deviate. These are basically known as rules.

• A. Linear: These functions have a specific range which exists from (-infinity, infinity) and a domain of (-infinity, infinity)

Example-

f(x) = 3x - 5

• B. Square

Example-

f(x) = 2xsquared + 4

• C. Greatest Integer

Example-

f(x) = integer(x)

• D. Constant

Example-

f(x) = 6

Explanation
I find that the easiest way to describe functions is to put forth examples and solve the examples step by step - thus teaching the general public how to process and solve a function equation. Functions are quite simple and usually only entail the plugging in of specific numbers. Functions can also be very complicated - which we will not go into because describing over a computer is nearly impossible. Functions entail domains which require the number line. Briefly speaking, I only presented the number line to make you aware of what it was - we won't be using it, only scratching over the surface. I'm not going to go into the logistics of the number line because that is achieved in basic math under the topic of inequalities. Basically the number line involves plotting points, shading inwards or outwards, and finding out domains - which are a specific set of numbers which the inequality is between.

Applying the Rules to Equations

• Let's use the equation "F(x) = |3x +1|- 6" for our example. The question states - What is the value of F(-2)
  Step 1. We are going to take F(-2) and plug it into the function, giving us: F(-2) = |3(-2)+1|- 6.
  Step 2. Secondly, we are going to multiply the 3 times the -2 and then add 1 which gives us -5, giving us: F(-2) = |-5| - 6.
  Step 3. Thirdly, The "| |" symbols mean absolute value. Absolute values should always be made into positive numbers thus giving us: 5 - 6 = -1, which is our answer.

• Let's use the equation "f(x) = x + 1 and g(x) = xsquared - 5". Find the value of (f of g)(4).
  Step 1. When working with a function of a function you work from left to right. So, we are going to take the (4) and plug it into the function g because that comes first. When we plug it in we get: g(4) = 4squared - 5.
  Step 2. 4squared is equal to 16. We then take 16 and subtract 5 which gives us 11.
  Step 3. Now we take the value which we got from the function g and plug it into the function f.
  Step 4. When we plug it into the function f we get: f(x) = 11 + 1, which gives us our answer of 12.

Graphs of Functions
Functions can also be graphed. To calculate specific points of intersection and location at specific points you may refer to a graph. Graphs of functions can also be found in the library of functions above. The library of functions graphs can be found here: http://www.wtamu.edu/academic/anns/mps/math/mathlab/col_algebra/col_alg_tut31_graphfun1.htm
These graphs will allow you to see the structure of the graphs of functions.

-Range-This is all the values which lie on the y-axis. This is the difference between the greatest and least value of data in a specific equation. The y values can be found on the vertical axis of the graph.

-Domain- When speaking in terms of the coordinate plane which is also known as a graph, these are all the x values on specific graph. The x values can be found on the horizontal axis on the graph.

 

[tyr0n3]

im not sure, but maybe you could inclue cos, sin and tan ratios.. as they are pretty easy. or maybe in a new/add one to this guide.

 

[Mr. Kroll]

im not sure, but maybe you could inclue cos, sin and tan ratios.. as they are pretty easy. or maybe in a new/add one to this guide.

Definitely.

Then you can move onto where Physics and Maths combine and start giving information on vectors and direction and magnitude.

I will be happy to help if there is anything you want a hand with.

 

[Graham]

Definitely.

Then you can move onto where Physics and Maths combine and start giving information on vectors and direction and magnitude.

I will be happy to help if there is anything you want a hand with.

I will include sin, tan, and cos, but I'm not writing a math text book here

 

[Mr. Kroll]

I will include sin, tan, and cos, but I'm not writing a math text book here

You're right, but including vectors is but one aspect of Maths. If you were to write a Maths Textbook, you would have to cover A LOT more aspects of maths, including the broad range of algebra.

 

[Graham]

This is far more complex than algebra though. Also, I'm not sure you're 100 percent sure of what you're talking about because vectors are more complex than this and aren't even the same subject.

 

[Billyy]

This is far more complex than algebra though. Also, I'm not sure you're 100 percent sure of what you're talking about because vectors are more complex than this and aren't even the same subject.

Yes, vectors are used in physics, and this is pre-calculus.

I took Pre-Calc in high school, but I didn't really understand most of it. Maybe it's because I had a shitty trig teacher the year before, because math builds on previous math skills.

 

[SuF]

This is far more complex than algebra though. Also, I'm not sure you're 100 percent sure of what you're talking about because vectors are more complex than this and aren't even the same subject.

This is more complex than Algebra? I am taking Algebra 2 online... And its much much harder than this...

But... This seems like a pretty good guide. I love the layout... Its so much better than many other guides I see now a days. Intending the paragraphs may make it look better though... But... Overall nice guide.

 

[Mr. Kroll]

Yes, algebra is a very broad subject.

There is some of algebra that is easier than this, but a lot of it is harder as well.

 

[`Failure]

This is more complex than Algebra? I am taking Algebra 2 online... And its much much harder than this...

But... This seems like a pretty good guide. I love the layout... Its so much better than many other guides I see now a days. Intending the paragraphs may make it look better though... But... Overall nice guide.

SuF - Generally, Pre-Calc is supposed to be much more challenging then Algebra II.

It really depends on how you get taught.

 

[Hippie_Slay]

Wow, I'm in algebra II and this stuff looks like something I've already learned. Couldn't be too hard.

 

[Graham]

Every school has different types of algebra, it depends on which section of algebra you're learning.

 

[BayBay]

I like this guide I find it helpful although I already have taken this class. I like the layout much better than most, and I also like the color variations. You could try adding on it a bit more, so it applies to a wider audience. Overall it is a nice guide that I think could help people which is more than I can say for most guides.

 

[liverpoolfan]

well aint i lucky i only take foundation

 

[Graham]

Usually, any topic which you've covered can be considered simple. When I see a guide which I'm well educated on the subject, I check to make sure they explained it thoroughly and in depth - although I already comprehend the topic. But thanks for the comments - positive/negative.