This week in math 10 we learned about graphing! First things first it’s important to understand what a variable is and that there are two types of variables, discrete and continuous. Variables are basically when the data or clues are given to us and it’s our job to find out where they go on a graph to showcase it a different way.
A discrete variable basically means a whole number / a number that you cannot divide. In other words, they don’t have an infinite number of values.A good example to remember this is how many people are in your household? As you cannot divide people in half (I would not like to see it anyway!), it counts as a discrete variable! Or maybe, how many cars sold from a dealership per month. As you cannot sell a fraction of a car, it counts as a discrete variable! When you’re graphing the dots and using a discrete variable, the dots on the graphs are not connected because the space between dots does not have value and there is nothing that is in between the dots on the graph as it cannot be divided.
A continuous variable meansthat there’s, in theory, an infinite number of possibilities. This variable is used to measure things like time, distance, weight, etc.The reason that they qualify as continuous is becausethey are not whole numbers. When you’re graphing the dots and using a continuous variable, the dots on the graphs are connected because the space between dots also has value.
This week in math 10 we learned about functions and relations!
First things first it’s important to know that Relations are 2 things that relate to each other.
Functions are like special relations. Per each input there is only 1 output. A good example to follow that of a mother to multiple children. Each child only has 1 biological mother, that is a function. Whereas a mother who has multiple children doesn’t have the same special relationship as a function (1:1) so it would be classified as relation.
You can see in the photo down below what a visual of relations and functions look like.
This week in math 10 we learned about how to evaluate a notation function. First things first, we need to know the different parts of the function. You can see in the photo below that every part has a label and as this chapter is mostly vocabulary based, it’s important you know what someone could be referencing.
There are a couple different ways that you can show your function, the first one im showing you is called ‘Mapping Notation’. The first thing you need to do is determine the ‘parent function’ aka the simplest form of that type of function, meaning they are as close as they can get to the origin
Next, you ask yourself, what changes in the equation? Or, what type of transformations are taking place in the equation. Let’s take a look at the example down below.
^and as you have the function you can write it in a product of ordered pairs to graph, ex. 2 ~~> (2, 10)
The next type of function notation we learned is simply called ‘Function Notation’.
Function notation is the way a function is written. It is meant to be a precise way of giving information about the function without a rather lengthy written explanation. o evaluate a function, substitute the input (the given number or expression) for the function’s variable. Replace the x with the number/expression. (Function notation is expressed very similarly to mapping notation.)
The last way we are showing is called ‘Equation’. the main part of Equation is that they aren’t names/ labeled so the only was to clearly showcase it is by writing it down visually. also keep in mind that saying ‘Find f (2) when f (x) = 3x, is the same as saying, “Find y when x = 2, for y = 3x.”