- Introduction -
In this I will have to investigate graphs of function and how their shape and position change the coefficient of the functions. I will have to describe what is going on in the table of graphs and I will write a conclusion that is reasonable.
The software I could use is MathCad or Microsoft Excel; I have decided to use Microsoft Excel because I don’t have MathCad software.
The investigation would be divided into four parts as I am going to show you:
Linear Graph- the equation I will use is f(x)=mx+c
For this I will have to select my own values for m and c and I will have to discuss the out come of my answer and I will have to describe what I can see.
Quadratic equation the equations would be f(x)= ax2+bx+c
This is roughly the same as the first part but I will have to change one value in this one and then I will have to describe what I could see.
Cubic equation= equation would be f(x)= ax3+bx2+cx+d
I will be able to change A and d if I want I wouldn’t be able to change b and c because that has to kept the same.
Reciprocal graphs equation would be f(x) a/x
In this part I will have to divide x by a, a would be the same number and x will change.
Out of all these formula I am looking at graph to see what is difference if I change a number or symbol e.g. plus I change it to a minus etc.
This is a preview of the whole essay
- What am I going to do -
Aim: investigate the functions in the graph also talk about shapes and the positions that has coefficients in the function. Then I would describe what has happened in the graph.
What I am going to do?
I would choose an x for a number and I would choose number for a, b, c, d if need so I can work on different graphs.
The function that I would be working on is Linear Graph, Quadratic, Cubic equation, Reciprocal graphs, so I could see the difference in each graph.
I would be using excel for this part not MathCad because I find Microsoft excel is easier to use because I am used to using Microsoft excel and I am used to the functions of it.
-Linear Graph y=mx+c-
I notice that when I changed the sign of c from plus to a minus the line just moves down the y-axis. I have notice that when I changed the sign of m from plus to minus it goes the opposite direction from f1.for f3 it increases rapidly compared to f1.
- Cubic equation- -
I have notice that f1 and f2 are the same I mean they both start with a negative number and they finish with a positive number, also f1 is increasing rapidly and for f3 going the opposite to the direction of f1 and f2 this is because I changed f3 to a minus x cube so this will cause it go to a different direction. This could be because I changed A number to a smaller number to see what effect it makes to f3 by doing this I also changed B, C, D because I wanted to see if I can get to curves in the graph but as you can see it created a two small curve and as to f1 and f2 it has one this is because for f2 I changed all the signs and all the numbers in it. I have notice that when I change my choices I can see a big effect because for f23 I have changed to a number to higher number then f1 and f2. this is because I wanted to see if I could get two curve lines in the graph.
Quadratic equations f (x)=Ax^2+Bx+C
I notice that when I changed the signs of A from plus to a minus the line just turns up side down because of the change in the plus and the minus. I change some numbers to see what I would get effect in the graph. With f2 I tried a different approach because I wanted a different answer to my graph but it also gave me a slope but this slope goes through the negative numbers only. For f3 it is a steeper slope because it’s a higher negative number. The effects that I had was because I changed the numbers but it didn’t make that much effect as f1 because for f2 I changed the signs and I double C to –10. But when I changed my choices A and B to a different number and I changed the sign it the answer I would get would have increased rapidly and decreased rapidly as well.
I notice that when my x is in negative the numbers it would end up in a positive number and also in a 2 decimal point number. But all the lines have a slope in side them. The slope isn’t a very big one but a slope in side it. The numbers stay the same for the negative and positive number. Both off the graphs are rapidly increasing but f1 is just faster because it’s a negative number also its bigger then five.
I notice that when my x is in negative the numbers would end up in a positive number and also in a 2 decimal point. But all the lines have a slope in side them. The slope isn’t a very big one but a slope in side it. You can f1 in the positive side has a bigger line then the negative line this is because negative divided by negative is a positive.
F2 is –14 I wanted to divide it by that because I wanted to see what impact would it have on the graph if I divide it by a double figure. You also can see that f2 rapidly increasing and a bigger steep then f1 because f1 steep is slowly going up.
In this conclusion I am going to talk about what I saw and I would compare both graphs to saw you what difference it made when I changed the sign and numbers around.
But for linear graph I didn’t use to graphs because the graphs would have looked the same as the first linear graph so I kept it as one graph.
Linear Graph - For this put have notice that when I had decided to changed the signs around from plus to a minus the line just moves a cross and for f3 it puts a line a cross for of the other to lines. So I add a f3 and that add a line through both of them. So by doing this I got a good graph to show.
Quadratic Graph- I have notice that f1 and f2 are the same I mean they both start with a negative number and they finish with a positive number, also f1 is increasing rapidly and for f3 going the opposite to the direction of f1 and f2 this is because I changed f3 to a minus x cube so this will cause it go to a different direction.
Cubic Equation- I notice that when I changed the signs of A from plus to a minus the line just turns up side down because of the change in the plus and the minus. With f2 I tried a different approach because I wanted a different answer to my graph but it also gave me a slope but this slope goes through the negative numbers only. For f3 it is a steeper slope because it’s a higher negative number.
Reciprocal graphs – for this I had done to graphs because I thought I can get different data, but as you can see the graph roughly the same but in the second graph you can see that f1 increases rapidly this is because the number is high negative number.