## Week 10 – Math 10

Although I was sick for half of this week, and wasn’t able to learn fully what the rest of that class did, or at least learned less “hands on”, I was still there for the first two days, and so what we learned then is what I understand most. We learned how mapping notation can be put into the form of function notation.

Mapping notation is where you use a math “sentence” to find an output with the use of an input. (went over semi-briefly on last blog post).

ex.

ƒ    :    x              →               3x – 2

name   input       changes into         output

Function notation is generally the same thing, but like how functions are relations but relations aren’t always functions, functions notation is the same. Function notation is helpful when finding inputs and outputs of functions. They are written slightly differently as well.

ex.

name   ↓input            changes into      output

ƒ         (x)             =                 3x – 2

“ƒ of x”

Both are used generally the same way, to find the output using an input. It is “ƒ of x” because the ƒ is the functions name, and the relation is a function.

Functions & Graphs

Using the inputs and outputs from mapping and function notation, you can plot points on a graph. The input is x, and the output is y. To get the output, you put the input in the correct spot on the opposite side.

ex.

f(x) = 3x + 1  →   f(3) = 3(5) + 1

Using them, you can get coordinates. (x, y)

## Week 9 – Math 10

This week we had our midterm and spent most of the week studying for it. But on Friday, we learned about functions, a kind of relation.

A function is a relation that is special and each input has one output, no more. A function is a kind of a relation but a relation is not a kind of function.

On a graph, if any of the points are on the same x axis, then it is not a function. Each point has to be in a different x coordinate.

ex.

A function is unique, and is often named a single letter (f, g, h, etc.), and followed by x, changing into blank.

ex.

ƒ:x  → 7x + 6

ƒ is its name, x is the input, the arrow signifies “changing into”, and the final numbers are the output.

## Week 8 – Math 10

This week we started our graphing and linear relations unit. One of the main things we learned was domain and range. The domain is all of the $x$ coordinates that the graph covers, and the range is all of the $y$ coordinates that are covered.

Domain and range can be shown in “curly brackets” such as in the following example.

{x|-4 ≤ x ≤ 7, x ∈ R}

Sometimes if the graph just contains a bunch of points, the domain and range can be given in specific numbers,

ex. D = {-2,0,1,4,7} or R = {1,3,4,9,12}

here’s what one of those graphs could look like:

But they can also be lines meaning their points can be anywhere on those lines,

ex. D = {x|-2 ≤ x ≤ 7, x ∈ R} or {y|1 ≤ y ≤ 12, y ∈ R}

here’s what one of those graphs could look like:

They can also be a line, but have no beginning and/or end. This graph would have lines with arrows to represent that it continues on.

ex {x|x ∈ R} or {y| y ≤ 12, y ∈ R}

here’s what one of those graphs could look like:

When writing in these curly brackets, especially with line graphs, you need to form a “sentence”. You start with the axis you are talking about (x/y), then the possible points, and then finish with x ∈ R or y ∈ R, which means x/y is an element of a real number.