Y=F(x+A) - How to calculate the equation

[dylan_shadowlocke]

In a previous question in my text book, I solved Y=f(x)+2 which is the same as Y=Y+2 so that very simply moved the whole graph up by 2.

I've been trying to solve this very simple equation, which i already have the answer to in my text book. I just don't understand it.

For the graph where f(x) is basically equal to y, and given the following points (x=2, f(x)=-1), (x=1, f(x)=1), (x=-1, f(x)=1), (x=-2, f(x)=-1)

How do I calculate y=f(X+2) ?

I know the "rule" is that i would move the entire graphed figure to the left, but I can't move past this until I understand a real math equation that will justify this so called "rule".

I've been ripping my hair out for hours over this!

Please help!

 

[stapel]

In a previous question in my text book, I solved Y=f(x)+2 which is the same as Y=Y+2 so that very simply moved the whole graph up by 2.

I've been trying to solve this very simple equation, which i already have the answer to in my text book. I just don't understand it.

For the graph where f(x) is basically equal to y, and given the following points (x=2, f(x)=-1), (x=1, f(x)=1), (x=-1, f(x)=1), (x=-2, f(x)=-1)

How do I calculate y=f(X+2) ?

They're using "y" to mean "the height of whatever points you're plotting". It may help instead to use different names. If you let the first function, with the points they've given you, be "f(x)", then maybe the new one could be "g(x)", so g(x) = f(x + 2). That is, the new function is the same as the old one, but with all of the points moved... two units in which direction?

 

[dylan_shadowlocke]

After careful consideration, I think that I am asking the question wrong. We already clearly have the equation. What i need to know is how you get from and to the following points using Y=F(X+2).

(x=2, f(x)=-1) TO (x=0, f(x)=-1),
(x=1, f(x)=1) TO (x=-1, f(x)=1),
(x=-1, f(x)=1) TO (x=-3, f(x)=1),
(x=-2, f(x)=-1) TO (x=-4, f(x)=-1)

Using the equation Y=F(X+2)

** I need to see all the steps and some examples using my numbers to fully grasp the concept, as I still don't get why adding numbers goes left and subtracting numbers goes right on the X axis. **

Does that make more sense?

 

[stapel]

After careful consideration, I think that I am asking the question wrong. We already clearly have the equation. What i need to know is how you get from and to the following points using Y=F(X+2).

(x=2, f(x)=-1) TO (x=0, f(x)=-1),
(x=1, f(x)=1) TO (x=-1, f(x)=1),
(x=-1, f(x)=1) TO (x=-3, f(x)=1),
(x=-2, f(x)=-1) TO (x=-4, f(x)=-1)

Using the equation Y=F(X+2)

** I need to see all the steps and some examples using my numbers to fully grasp the concept, as I still don't get why adding numbers goes left and subtracting numbers goes right on the X axis. **

Looking at the function-transformation rules they gave you, and using g(x) = f(x + 2), in which direction are the new points g(x) moved, relative to the old points f(x)?

 

[dylan_shadowlocke]

The new points are moved to the left when X is positive and to the right when X is negative, which is the opposite of what you would think. I really was hoping to mathematically justify it since its an equation and its only going to get more complex from here.

I will end up not understanding it as it gets more complex if i cant somehow add the +2 to something and logically see why it subtracts rather than adding which is what the plus sign is for...

 

[stapel]

I will end up not understanding it as it gets more complex if i cant somehow add the +2 to something and logically see why it subtracts rather than adding which is what the plus sign is for...

They added 2 to the x-value. What do you have to do to the x-value, in order to take the argument back to where you'd started?

 

[Ishuda]

The new points are moved to the left when X is positive and to the right when X is negative, which is the opposite of what you would think. I really was hoping to mathematically justify it since its an equation and its only going to get more complex from here.

I will end up not understanding it as it gets more complex if i cant somehow add the +2 to something and logically see why it subtracts rather than adding which is what the plus sign is for...

Think of the (rigid) graph of f(x) and now you are going to move it either left or right to produce g(x). So grab a hold of the graph at x equal 1 and move it to the right 1 space and look at the x value. It is 2. What do you have to do to the 2 to change it to a 1 [so you can get f(1)]. It isn't what you are going to do with the x you moved from [the x of f(x)], it is what you are going to do with the x you are at [the x of g(x)]. Yes, I had to think about that myself for a while.

 

[ksdhart]

Here's another way of looking at it that may or may not help you. Let's say you have a function f(x)=x². And then g(x)=f(x+2) or (x+2)². I'll plot a few points first:

x=0
f(x) = 0^2 = 0
g(x) = (0+2)^2 = 2^2 = 4

x=1
f(x) = 1^2 = 1
g(x) = (1+2)^2 = 3^2 = 9

And so on... Now if you plot more points, you'll begin to notice that for any value of x, the value of g(x) will be higher than f(x). But instead of looking for some values of x, what if we look at some values of the y-coordinates?When f(x) equals 16.... f(x) = x^2 = 16; x = 4

When g(x) equals 16... g(x) = (x+2)^2=16; x = 2

Now if you plot those two points, you get (4, 16) and (2, 16). Those are two points with the same y, but the point on g(x) is shifted to the left, relative to the point on f(x).