CH 1 Graphing Functions by Thanh Quotient

So for my Graphing Function in Ch1, I chose f(x)=|x| show on the left. First off I graphed the original function f(x)=|x|, the Coordinates for the X-axis which is also known as the horizontal line is Zero(0) and the Y-axis which is known as the vertical line which was also Zero(0). After graphing my original function in black above the X-axis I started graphing some transformations of the original function. I drew the following Translations of f(x)=|x - 3| in blue , f(x)=|x - 3| + 4 in green, and
f(x)=|x| +4 in red, But before we go any further its important to know that f(x) is also another way to represent the Y-Coordinate. So what i did is when i graphed the translations f(x)=|x -3|, I moved from the coordinates (0,0), i moved right by 3 units. The function f(x)=|x - 3| + 4 i used the same trick as i did for the first function, i moved from the coordinates (0,0) to the right 3 units but this time I went up 4 units. Now your probably wondering how would you know when to move up or down or left or right, so the trick I came up with is when there are numbers in the groupings, absolute values, square roots or in anything as long its not left out of something like (x + 3) you know that the number inside is affecting the X-axis which is also known as the horizontal line, But, the tricky part is that when you have a positive number like +3 you move left instead of right but if its -3 you move right instead of left. But for the Y-axis also known as the vertical line if its +3 and its outside of the groupings and such you go up and -3 you go down, yes this is confusing BUT its a good way to remember, Just remember INSIDE AFFECTS INPUT WHICH IS KNOWN AS THE X-VALUE AND OUTSIDE AFFECTS THE OUTPUT VALUE. So for f(x)=|x| + 4 (remember the 4 is outside) we move from coordinates (0,0) up 4 units. Also if you have not figured out by now, Coordinates are the X-values and the Y-Values, as you probably know, the values affects your place in units. Now off to the Reflections all you have to remember is that when you have a negative such as f(x)= -|x| you flip the original function across the X-axis also known as the horizontal line and the outside numbers just affects how high or how low your function should be placed; However if you want to flip a function across the X-axis and your normal function is a Negative, you turn the f(x)= -|x| from negative to positive which will give you f(x)=|x|. BUT IF you wonder how you reflect the function across the Y-axis all you do is make the signs opposite for the outside numbers, for ex. if you had
f(x)=|x| +4 all you do is change the + into a - which means f(x)=|x| - 4 would be flipped across the Y-axis. So the reflections for my graph were all below the X-axis and the reflection of the original function f(x)=|x| was purple.

By Thanh Quotient