**PROBLEM # 1**

I noticed that the vertex of the graph moved upward or downward when constant is added from the original equation ( y = x^2 ). And it moved left or right when the constant in x then squared.

**PROBLEM # 2**

I noticed that the minimum and maximum of the waves of the graphs changes depending on the numerical coefficient of cosine and x.

**PROBLEM # 3**

I noticed that the graph y=ln x is asymptotic to the y axis while the graph of y=e^x is asymptotic to the x axis.

**PROBLEM # 4**

**PROBLEM # 5**

**PROBLEM # 6**

y < (-1/5 x) +4

x > 0

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Here is a picture or diagram showing the set of REAL NUMBERS. This picture includes the members of the real numbers. Real numbers is divided into two groups, the ** rational numbers** and the

**. Under the rational numbers are the**

*irrational numbers***integers**which includes zero (0), positive and negative numbers, the

**whole numbers**and the

**natural numbers**or the counting numbers starting from 1,2,3….. While under the

**are the**

*irrational***non-repeating decimals.**

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Just like a typical contest, having Mathematics in my life comes in easy, average and difficult round. When I started schooling, I thought that Math is just about learning how to add, subtract, multiply and divide. But I was wrong. I learned that Mathematics is a broad subject that needs a large understanding and analization. But still, I started to love and appreciate the subject at my young age.

I’ve been our school’s representative in several math competitions since elementary. Because of that, Mathematics served as my breakfast, lunch and dinner everyday. ^^ My teachers trained me whole day. I also attended review and advanced classes as preparation for the contest. I learned different ways and techniques in solving Math problems. For most people, dealing with numbers and computations is really a burden. Math is really difficult to learn and understand. But as a Math-lover, it’s just a matter of appreciation.^^