This week in Math we learned how to add and subtract rational expressions. To add and subtract rational expressions, we must first find a common denominator and then make the numerators equivalent and then simplify.
Ex.
This week in Math we learned how to simplify equivalent fractions.
To simplify these type of fractions, there are 3 steps.
Ex.
Article:https://www.nytimes.com/2018/04/30/upshot/worried-about-risky-teenage-behavior-make-school-tougher.html
This article is about the correlation between the difficulty of school and risky behaviour among teens. This article interested me because of how school is currently affecting my life and I was interested to see what is happening on a broader spectrum. The author had a good style and writing because he was objective and because he expressed his points through the example of graduation requirements changing, requiring more courses and as a result risky behaviours such as drinking have dropped among teens. This article raises the question: Should school be harder to try eliminate bad behaviour for good? I think that no matter how hard they make school, there will always be some kids who don’t care about there future and will not try and get into bad habits, but for regular kids who care about their future this could be a positive thing for them in the long run and gives them less opportunity for risky behaviour. It also will make kids mentally stronger and more resiliant for future challenges when they go to university and will all-round improve the rate of advancement in society, since kids will generally become smarter.
This week in Math we learned about reciprocal functions. The reciprocal of a number would be the inverse of its fraction form, for example the reciprocal 2/3 would be 3/2. So for reciprocal functions, if we have the parent function y=x, then we change that to y=1/x.
The above graph represents the function y=1/x. If you had a table of values representing this function you would notice that as the x value increases, the y value decreases getting ever closer to zero but never reaching it and as the x value decreases below 1 than the y value approaches infinite; and then the second line does the same thing except in the negative section of the graph. The lines formed by reciprocal functions are called hyperbolas.
When graphing, the points 1 and -1 on the y axis are very important. Because the reciprocals of these numbers are the same as the original number, on the graph these are known as invariant points. The linear parent function y=x will only intersect at the invariant points and this function is very helpful when graphing.
Since the hyperbolas will always approach zero, but never reach it, we call the line that it will never cross an asymptote. There is a horizontal and a vertical asymptote. Because this is the parent function, the asymptotes will just simply be the x and y axes, so you would say the vertical asymtote is x=0 and the horizontal y=0.
This week in Math, we learned how to graph and interpret graphs of absolute value equations. Since absolute value generally means that a number will always be expressed as a positive value, then the output values of our graph will always be positive. Below is what the graph of the parent function looks like.
As you can see, the y value will always be greater than or equal to zero.
To express the equation without absolute value symbols we use what is called piecewise notation.
For the parent function, it would be:
The line on the left is simply the opposite (negative) version of the linear parent function y=x.