# 8 paragraphs Math 600 words total

Respond casually to ech paragraph. you can agree, add your opinion, add related knowledge, or answer the question if there is one.

75 words

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Order Paper NowThere are many videos/tutorial also on the internet. Just put what you need in a search engine and the world is at your doorstep. 🙂

Here are a few to get you started:

Khan Academy. (2012). *Introduction to functions*. Retrieved from http://www.khanacademy.org/math/algebra/algebra-functions/v/introduction-to-functions

Purplemath. (2012). *Operations on Functions. *Retrieved from http://www.purplemath.com/modules/fcnops.htm

Purplemath. (2012). *Composition of Functions: Composing with Sets of Points.* Retrieved from http://www.purplemath.com/modules/fcncomp.htm

I hope these are useful to you! 🙂

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75 words

Class,

Once you memorize and get familiar with these procedures, it is helpful to practice, practice, practice … Such combinations of letters can be very confusing at first.

Here’s an example:

Decide whether each relation defines a function.

H = {(2, 3), (4, –1), (–3, 5)}

H is a function, because for each different x-value there is exactly one y-value.

{2, 4, -3} does not correspond to

{3, -1, 5}

Class,

For two functions: f(x) = x + 5 and g(x) = x^{2 }+ 3, what does the notation f(x) and g(x) mean? Why are we not simply using y as we did before?

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75 words

You seem to grasp this very well. Thanks! 🙂

Class – refresher …

Take a look at this example about what is and is not a function …

J = {(3, 1), (3, 4), (3, 6), (4, 5)}

{3, 4} does not correspond to

{1, 4, 6, 5}

So, J is **not **a function because one first component corresponds to more than one second component.

Class,

For two functions: f(x) = x + 5 and g(x) = x^{2 }+ 3, is f(x) = x + 5 a function or a relation? How do you determine that?

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75 words

I would prefer to use the addition operation when solving functions. Addition is a simple process that we learn at a very early stage in life. When adding functions one would take the two problems that the functions represent and add those equations together. When subtracting one would have to determine if in the end it would result in a positive or negative number, multiplication must include the distributive process and then grouping like terms. Division could result in a few ways, most times it could stay as the way it was first written, or it could be broken down. In this case the most difficult process would be multiplying functions. Multiplying functions has the most steps required, and if a step would be forgotten then the solution would be wrong. I hope I provided the correct information. Please let me know if I was wrong, so I could correct my mistakes, and be aware of those areas.

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75 words

I think that the majority of the people are going to write “addition” because overall it requires less work of the four. That is also my answer because of that. I think that it is the easiest to perform because I can (most of the time) do addition in my head without using a calculator. With multiplication, you have to use the distribution process. With division, you have to break the numbers down, which could get hard with larger numbers. Subtraction could be tricky because you have to remember the negative sign, which I have forgotten about a couple of times. All four methods require work and carefulness because one number off will throw off the whole equation. I guess it just depends on who you are because I am sure that someone will say that subtraction is easier for them.

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75 words

I agree most of us will chose addition as the easiest I think it is because it is the first thing that we learned in grade school in math class.* *I also think that the subtraction part is just as easy because again this was the second thing we learned in math in grade school. They go together the division part is a little more difficult due to you have to figure out what goes into each number and how you can solve the equation.

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75 words

The process I find to be the easiest is the addition part. This is basically the first thing that we learn when we start school is to add one number with another. I think that it is easy because it just comes naturally and with that we can solve the problems. The one that would probably be the more difficult one is the division part because you won’t always have a number that divides evenly and with that you need to work a little harder to figure out the answer(solution). What do you think is the most difficult?

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75 words

When working with the functions, adding, subtracting and multiplying, are all about the same depending on the numbers in the function. I do not really find one of them easier than the others. The process is pretty much the same, once you get used to it. Paying attention to whether a number is positive or negative seems to be my biggest challenge. Division I do find to be the most difficult.

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