CH1 Graphing Functions

The graphing function I used is f(x)=|x|. When you are graphing this you start at point (0,0). If you want to move the function left or right on the x-axis, it is called a transformation. And if you want to move the function up or down on the y-axis, it is called a translation. For example: I want to graph f(x)=|x|+5. This would be a translation because the function moved 5 places vertically. Another example is if I wanted to graph f(x)=|x+8|. this would be a transformation, because the function moved 8 places horizontally. When you want to graph refections there will always be a negative sign(-) before the absolute value sign(|x|). This reflects the function across the x-axis.

CH1 Graphing Functions

My graphing function that I chose was f(x)= |x|. I started out by graphing my function in black to identify it as my original function. Opening upward, this function starts at the origin, (0,0) , of the graph. To start off, this function can have many types of transformations. The first transformation, shown in red, is a vertical translation 5 units up the y-axis. By doing this, it changes the function into y=|x|+5. The next transformation, in blue, is a horizontal translation to the right on the x-axis by 8 units. This turns the function into y=|x-8|. Illustrated in green, y=|x-8|+2, shows an example of a combination of both types of transformations. A horizontal 8 units to the right and a vertical shift 2 units up. Furthermore, illustrated in purple, y=-|x|, shows the function reflected across the x-axis. Lastly, in black again, portrays all three types of transformations. A reflection across the x-axis, a horizontal shift 6 units right, and a vertical shift 2 units down resulting in y=-|x-6|-2.

Graphing Function CH1 By Princess Geometry

For my graphing I chose to do y=x^2 at the origin (x-axis 0 and y-axis is 0). Second I made a transformation which is the vertical translation 4 units up making the equation y=x^2+4(purple). Then I started from the original function and made a horizontal translation 5 units to the left making the equation y=(x+5)^2 (Pink).Next starting from the original function I did a horizontal-vertical translation 6 units left and 2 units up, making the equation y=(x+6)^2+2(Red). Starting from the original function again I graphed a vertical reflection across the x-axis, making the equation y=-x^2(blue). The last one I graphed was a horizontal-vertical,and reflection translation 6 units to the left and 2 units down, making the equation y=-(x+6)^2+2(orange)

Graphing Function

The fuction I choose on this graph is the absolute value fuction, which is y=x draw in black, after this I can do Transformation to the function which is changing it from the orginal. To graph the reflection of y=x multiply by (-1), you get y=-x draw in purple above. After the vertical translation, shift 5 units up, it can be written as y=x+5; in the graph above the whole thing move up in the vertical line-the coordinates for the y-axis is 5. For horizontal translation it was also shifting 5 units, but not on the vertical line but on the horizontal line-the coordinates for the x-axis is 5,because y=x-5 it has a subtract sign inside so we move it 5 units to the right from 0. Combining horizontal and vertical translation it can be written as y=x-5+5 ,the +5 was outside so we shift up on the vertical line then right 5 units because there is the -5 inside. To graph the reflection of the function after the horizontal and vertical translation you have only have to multiply the whole thing with (-1) then you get y=-x-5-5.

Graphing Functions

The Function i chose to graph was y=x^2. First, i graphed y=x^2 at ( 0 , 0 ) because that's where the original functions starts. Then i made a transformation to it which is Vertical Translation up by 4 units and the equation would be y=x^2+4 (Red). Then i would go back to the original function and made a Horizontal Translation left by 9 units and the equation is Y=(x+8)^2 (Blue). And Again, i would start back from the beginning and made a Horizontal-Vertical Translation 9 units left and 4 units up and the equation is y=(x+9)^2+4 (Green). I Then made another transformation called reflection across the x-axis who's equation is -y=x^2 (Purple). And lastly i made a Horizontal-Vertical-Reflection across the x-axis and i got -y=(x+9)^2+4 (Black) as the equation.

Graphing Functions

The Graphing Function I chose to do was y=x^2. First off, I made y=x^2 at the origin (X-Axis 0 and Y-Axis 0) since this is where it starts . Secondly , I made a transformation which is the vertical translation by 3 units by 3 units up and the equation would be y=x^2 +3 (Red). I would then start from the original function to make a horizontal translation 5 units to the left so it would be y=(x+5)^2 (Blue). Next, I would do a horizontal-vertical translation which is moved to left by 5 units and up by 3 units so it would be y=(x+5)^2 +3 (Green). Starting from the beginning again I made a vertical reflection x-axis and its function would be y=-x^2(Purple). Lastly, I made a horizontal, vertical, and reflection translation from the start to get y=-(x+5)^2+3 (Black).

Graphing Functions

I used y=x^2 (black) as my graphing function and its vertex is located on the 0 of the y-axis and 0 on x-axis, which is the origin. The first transformation I performed was the vertical translation (red). To perform the vertical translation, all I did was to add 3 to my original graphing function, which makes it y=x^2+3 and on my graph, I only have to move the graphing function 3 units up. Next, I made a horizontal translation (blue). Since I moved the function 4 units to the left, my new function is y=(x+4)^2. In horizontal translations, you do the opposite of the other, which means that if its negative, you move to the right and you move positive to the left. After performing the vertical translation and the horizontal translation, I now somewhat combine them and turn them into something called a vertical horizontal translation(green). So I moved the function 3 units up and 4 units left and new function would be y=(x+4)^2+3. Then I made a vertical reflection (purple) across x-axis. To make a vertical reflection, all I did was to multiply the graphing function by negative and my new function would be y=-x^2. Lastly, I performed a vertical horizontal reflection (black). Like the vertical horizontal translation (green) I did, now I just have to multiply it negative and voila, there is my new vertical horizontal reflection y=-(x+4)^2-3.

Graphing Function CH1 By Zekai Function

The graphing function I did was y=³√x which was drawn in black. Then I did a vertical translation by 2 units which shifted up by 2 units and the equation was y=³√x +2. It was drawn in red. Then I showed a horizontal translation by 4 units which shifted to the left by 4 units and the equation of this function was y=³√x+4 . It was drawn in blue. Then I performed the combining vertical and horizontal translation which was drawn in green. In this translation, I shifting 4 units up and 4 units to the left. Its function became y=³√x+4 +4 . Then I did a reflection across the y-axis which was drawn in purple. Its equation y=-³√x. Lastly, I did a combining translations and reflections which was also drawn in black. In this function, I made a reflction across y-axis and shifted up by 2 units. Its equation became y=-³√x +2.

Ch 1 Graphing Functions

Note: Graph one is my mother's
Graph two is mine

1.) The graphing function I used was y=x^2 (black) it crosses the x-axis as shown on the graph. Then I decided to graph the reflection (purple) y=-x^2. For a reflection all you do is graph the opposite of the original function that's why x is negative. Next is the vertical translation (red) this one crosses the y-axis. The function for this is y=x^2+3 all you do for this is move up 3 making it vertical. For the horizontal translation (blue) y=(x+4)^2. For this transformation a positive 4 is graphed on the negative side. on the other hand, if it were to be a negative 4 then it would be graphed on the positive side. Next for the vertical and horizontal translation (green) y=(x+4)^2+3. This transformation is actually easier then it looks, first you move over 4 (negative x-axis) and then shift up 3 (y-axis). Finally for the vertical, horizontal and reflection translation i graphed y=(-x+4)^2+3. the x is negative because it is a reflection but is also shown drawn on the y and x-axis.

2.) This is what my mom came up with at back to school night. It seems she was confussed because I explained the instructions vaguely and then told her to start drawing. But I actually did a good job explaing hoe to graph transformations because she dre the graph better than me.

Ch 1Graphing Functions

By Ellie Cosine
My original function was y=√x which is in black. My reflection which was in purple is y=-√x it is the same but it's just negative. My vertical translation (red) is y=√x+12 for this one i just added 12. My horizontal and vertical translation (green) is y=√(x+4)+10 for i just graphed it on the points (10,4). My horizontal translation (blue) is y=√x+14 for this i just graphed (14,0). My reflection, horizontal, and vertical translation is y=-√(x-4)+10 for this i just graphed (-4,10). These are all of my transformations.

Ch 1 Graphing Functions

The graphing function I chose was y=x^2. I started off by drawing the original function which is in black. The original function crosses over the y-axis. Then I did a vertical translation by 3 units which moved the function up by 3 units and so the function's equation becomes y=x^2+3, this graph is in red. Then from the original function, I performed a horizontal translation by 4 units which moved the function to the left by 4 units and is graphed in blue. That function's equation became y=(x+4)^2. I combined the two previous function equations to perform a vertical & horizontal translation which is in green. To do this transformation, I moved it up by 3 units and to the left by 4 units which became y=(x+4)^2+3. Then from the original function, I made a vertical reflection across the x-axis which is in purple. This function became y=-x^2. Finally, I made a vertical, horizontal & reflection translation which is also in black. This function became y=-(x+4)^2+3, which is on the bottom left.

Ch 1 Graphing Functions

By: Maryam Integers

In this graph, I used the parent function of x to the second power (graphed in the color black). This graph has many transformations. They include vertical translation (red) which is when I moved the graph 3 units down (y=x^2-3), horizontal translation (blue) Which is when I moved the graph 4 units left (y=(x+4)^2) , vertical + horizontal translation (green) when I moved the graph 3 units down and 4 units left (y= (x+4)^2-3), vertical reflection across the x-axis (purple) when I flipped the graph upside down (y= -x^2) , and vertical + horizontal reflection across the x-axis (also black) which flipped the graph (y= -(x+4)^2 +3)upside also. When you perform a reflection across the x-axis the points on the y-axis change.

Ch 1 Graph Functions

I graphed the functions on the graph f(x)=x. I marked points from the function on the (x-axis horizontal) and the y-axis(vertical). Mark the points from the end of the vertex then make a reflection on the end of the other vertex. A reflection f(x)= -x). When it reflects you change it to negative. The red in the graph f(x)=x + 3. Then to graph you move up 3 units. Then you move down 3 units to form a translation. The other function is f(x)=x + 4. When the function is on the x axis moving right or left it is a transformation.

Ch 1 Graph Functions

What I done was graph the functions on the graph(f(x)=|x|. I marked points from the function on the corresponding x-axis(horizontal) and the y-axis(vertical). All I had to do was mark the points from one end to the vertex, then make a reflection on the other end of the vertex. A reflection (f(x)=-|x|). When it reflects you change it to a negative. The red in the graph is (f(x)=|x| + 3). Then to graph it you just go up 3 units. Then you go down 3 units to form a translation. The other function is f(x)=|x + 4|. This is a transformation, when the function is on the x axis moving right or left.

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

Ch 1: Graphing Fuctions

First thing I did was draw the function y=3√x (Square root). Then I drew a reflection across the y-axis, making the function y=-3√x (square root) in purple. Then I drew a vertical translation which moves the equation 3 units up in red and the equation was y=3√x+3. Then I drew a horizontal translation in blue, moving the function 4 units to the left along the x-axis and the equation was y=(√x=4)3 (exponent). Then I drew out a vertical and horizontal translation moving 4 units left and 3 units up in green, and the equation was y=(√x=4)3 (exponent) + 3. Last function I drew was a transformation in black by using vertical and horizontal translation then the reflection across the x-axis to reflect the original function across the x-axis then moving it 4 units left and 3 units down. The equation was y= -(√x+4)3 (exponent).

Donald Polygon

The graphing function I used is shown in the picture to the left, which is f(x)=|x|. First of all, its best to start on a graph. If you haven't known already, you need to start off with a x-axis and a y-axis. To be even more specific, the horizontal line is the y-axis and the vertical line is the x-axis. Moving on, f(x)=|x| would look similar to a V. Start the point and (0,0) and draw yourself a V. The red V shown in the graph is f(x)=|x| + 3. The reason why the 3 is not in the absolute value is because its not moving the V to the left or right. When it moved up and down, it is a translation. To draw that V, you basically move the entire V from (0,0) 3 units up. So count three squares and draw the V there. Now to draw f(x)=|x + 4|, it is called a transformation, because you are now moving the V left or right. Same thing with the translation, the way your moving your V, but for f(x)=|x + 4|. Take your V from (0,0) and move it to the left 4 squares. Now to do a reflection, use the purple V as an example. f(x)=-|x|. You will always know that functions with a negative symbol will be in the negative y-axis.

CH 1 Graphing Functions

NOTE:
-Top picture is what I did.
-Bottom picture is what me & my mom did during back to school night.

1. I first sketched out the function y=√x (Square root) as you can see in black. Then, I sketched a vertical translation moving 6 units up along the y-axis in red, and the equation was y=√x+6. After that, I sketched a horizontal translation moving 10 units to the left along the x-axis in blue, and the equation was y=√x+10. Then I sketched out a vertical and horizontal translation moving 10 units left and 5 units down in green, and the equation was y=√x+10-5. After that, I sketched a vertical reflection across the x-axis in purple, and the equation was y=-√x. Last, I sketched a transformation by using vertical and horizontal translation and the reflection across the x-axis to reflect the original function across the x-axis and moving it 1 unit left and 1 unit down which came out to y=-√x+1-1 in black (not the original function).

2. First off, she ask me what is she doing. I told her graphing functions. Well, it was hard translating in Chinese to her. But after I did the original functions, I taught her step by step on how to graph the functions. She then understood and started to graph as I told her to. At the end of the night, she learned how to graph function.