What we learned this week builds on my last blogpost as this one uses the last method within it. Last week we would used a different function (y) it can be mixed up so pay attention, to represent the outputs and range of the relation, but in this week we use f(x)= to represent the function instead. To use function you basically just input your numerical x value anywhere in the equation where x is already then you solve. Using function notation you can find lines and unknown co-ordinates because of the input abilities. Down below I have shown you how to use function notation to input plots on a graph, and the difference between function notation and x-y notation.

This week we learned about functions. Functions are related to domain and range because they are what make it up (relates them through an equation). You use it by using the replacement for x and y in equations to find the opposite. It can be tricky though to spot this special type of relation because each element of the domain is related to exactly one element of the range, which can be hard to spot sometimes. Im going to show you all the methods you can use to spot what relations are real functions. First you can see using an arrow diagram, the rule is if more than one arrow leaving an input number to an output means it is not a function, then ordered pairs, if the input value (x,y) shows up more than once in your sequence then it isn’t a function, and lastly in graphs you can find out whether it is a function by using the vertical line method, using this method you can find a “fake” function by seeing if any vertical line drawn on the graph intersects more than once on the graph then it is not a function. Down below I have shown you examples of spotted non-functions and real ones.

This is a change up to the math we’ve been dealing with recently as it offers a way more visual component to it. It taught me how to further deal with expressions through input and output (putting numbers into a variable to see a different outcome). It is a skill that can be used in things like graphing etc. and using input and output methods using graphs, ordered pairs, table of values, and mapping diagrams which overall just show the relation between the independent and dependent variables. Below I have showed you what the different methods look like, as they’re plenty to choose from which can make it easier to find which one is best suited for you, makes the most sense.

Throughout all the chapters we have learned so far many connections can be found that can be used to create memorization techniques. I have chosen to show you the connection I made between GCF and LCM and the polynomial unit we just recently looked at. Looking at knowledge from previous units that we are able to place on the next really allows for deeper understanding of a topic. In the most recent unit we studied (polynomials) I came across factoring, which I found decently easy when it came to the basics but then we go to further factoring with larger numbers and it started to confuse me, as it just looked to be to much. Then I started to look at it using a different perspective which really allowed me to understand it, once I started being able to see that I only needed to find the greatest common factor between these numbers is what really made it clear. Below I have shown you an example; which although make look very large (number wise) can actually be very small (using GCF).