This semester has been great because I have learned the new things that taught me for future use! It’s thanks to my teacher, so here’s the most important things that are flowing in my mind.

• Prime Factorization has taught me to find the prime and the composites in a large number to get to the GCF and LCM, which helps me to evaluate the numbers and it’s easier to get to the answer. What’s easier to remember is that the GCF is to find the “couples” also known as the pairs of prime to multiply through your answer that represent the largest integer through two numbers. While the LCM is to find the couples and the lonely people, who doesn’t have a pair to represent the smallest integer that share the common numbers to become as the LCM. They are to divide into the numbers, which is why it’s easier to go through these process with a large number from factorization.
• What’s essential to cover in career paths, weather that’s involving in astronomy for gravitational field, or building a structure for the people was using the work of trigonometry. This helps me to discover the unknown sides with the Pythagorean Theorem (a²+b²=c²) that was taught in ninth grade and it continues on to your courses! However, you must have two sides that have given you the measurement in order to solve. When there’s a path of the functions for trigonometry, then it automatically clicks to my brain that I was curious to know about the buttons that were on my calculator. It wasn’t hard that to find an angle, you click the button of the three ratio, which are sine, tangent, or cosine with a negative one of the shift key. This gives you the angle of the triangle that depends on the angle of elevation or depressions. And that’s how trigonometry were teaching some new vocabularies for me!
• As you can see factoring has taught me the key to expand my brain power by knowing the rules of them. The first rule was the look for the GCF, and the second rule is to get into the conjugates that makes the sum to disappear. As for example, (x+5)(x-5) would lead as (x²-25) of the FOIL method, which have introduce me to multiply in every variables of the bracket. Then the last rule was 3 terms that leads you to the x², the sum that adds up to, and the constant that are multiplied from the two numbers. Although, they were difficult to solve the numbers, but it adds up to my knowledge of teaching to others.
• When the functions has f(x) with the y- intercept from, it has lead me into confusion as to why would they do that? They are special, because they have their own name and it’s to tell the difference between relations.“This image is indication that functions can be a relation, but not all of them are.”  Furthermore, the relation has the ability’s to make a order pair with another one that have the same integer as the domain value. Which leads to their graphing as different than what we usually see in a function, with their curved line on the graph. Certainly, we would use the vertical line test to determine that two points in the line would lead to a relation.
• Since, we are talking about graphing then why not to know that the rise and the run, that is our slope is causing our points to be drawn. Specifically, we are looking for weather the slope is a positive or negative, which impacts the line that I tend to mistake on my tests that are given. It’s important for me to know the features of the Slope Guy, who’s my boyfriend that thanks to his handsome face, it have taught me to use in graphing. As for example, the undefined (x,0) was creating a vertical line, while the zero slope (0,y) makes a horizontal line that passes through each value. Therefore, it makes more for the slope that a parallel is to cause the slope of two equation to be the same, and the line are in equal distance to each other. While the perpendicular makes an impact of the two slopes, where one is flipped to their reciprocal that’s negative from a positive slope. We are to permit that the perpendicular line is suppose to form a ninety degree to intersect as a right angle. Regardless, these vocabularies has taught to draw a line on the graph without the fear that I have been struggling in ninth grade.