Creating Linear Transformations: Drawing Arbitrary and Transformed Graphs

[mjwess]

i need to draw 2 graphs, one arbitrary graph I make up that is not a normal distribution, and then i need to draw another in which i apply the linear transformation Y = 4X +2. I know that all the heights need to go down to 1/4 of the origional, but I don't know if it needs to shift to the right by 2, or if I need to plug in all the x values to the equation and shift them over by that amount


please, can anyone help me?

 

[Dick]

Uh, Y=4X+2 is not a linear transformation. It's a linear function. Do you mean first draw the graph of y=f(x) and then draw the graph of y=f(4x+2)? I'm a little confused.

 

[mjwess]

my mistake

here is the problem that was written down on the paper:

draw a distribution curve, something other than a normal distribution, labeling the x and y axes carefully. let yor x distribution (an idealization of the density histogram for some date values x1, x2...) we will apply the linear transformation Y = 4x +2 to the data. Draw the distribution curve for the Y data (the linearly transformed data) carefully labeling the x and y axes, and explain how this curve compares to the distribution curve for the x data



and how much does the graph shift on the X axis? 2 or more or what? please...and thank you...

 

[Dick]

Ok. So the magic word is 'histogram'. I think. The vertical coordinate represents density of the x points. I think. Now you want to draw a histogram for the set where each x is replaced by 4x+2. I think. One thing that is true is that the density drops everywhere by a factor of 4, right? Ok, but now the density value that used to be at x=0 moves to x=2 (and decreases by a factor of 4). The density that used to be at x=1 moves to x=6 (and decreases by a factor of 4) etc etc. So the graph doesn't just shift, it shifts and scales.

 

[mjwess]

thank you soooo much youre a great help! is there like a "give Dick a good rating" button somewhere?

 

[Dick]

You just pushed it. Thanks.

 

[mjwess]

i did? how... just by saying youre a great help?

 

[Dick]

Well, yeah. There's no centralized rating system. But the people that run the forum do read threads. How do you think I got all these awards I didn't ask for?