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Transformations of Functions- graphing y=f(x)-4?

  1. Mar 28, 2007 #1
    How would you graph y=f(x)-4? I am not sure how the original graph looks like y=f(x) either. Also, if i were to graph this using a graphing calculator, how would that be done?
     
    Last edited: Mar 28, 2007
  2. jcsd
  3. Mar 28, 2007 #2

    cristo

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    Erm.. you need to know what f(x) is. f(x) can be any function of x, so it is impossible to sketch it until you say what it is!
     
  4. Mar 28, 2007 #3
    I think the answer kumar wants is:

    You take the graph of f(x) and shift it down four units. (Assuming f:R->R).
     
  5. Mar 29, 2007 #4
    I think ZioX is right. From what I remember, f(x) is the same thing as y so it's saying (IMO): y = -4. So it would be shifted down 4 units and you should have a horizontal line.
     
  6. Mar 29, 2007 #5

    cristo

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    Well yes, but in the original post he says he doesnt know what the graph of the function f(x) looks like. Thus, he will need to plot that first then shift it four units down.
     
    Last edited: Mar 29, 2007
  7. Mar 29, 2007 #6

    cristo

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    Huh? That's not what ziox is saying. How do you get that the graph is even a straight line? We do not know the form of f(x). It could be f(x)=x^2, in which case y=x^2-4; clearly not the straight line y=-4!
     
  8. Mar 29, 2007 #7
    In a graphing calculator, you should graph this cristo: y = f(x) - 4 and you will get a straight line 4 units down. It's going to be a horizontal line and the coordinates would be: (0,-4). I tried it and that's what I got. Maybe I did it wrong but I'm not completely sure about it.
     
  9. Mar 29, 2007 #8

    cristo

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    Your calculator is assuming f(x)=0, since you have not defined it, thus it sees the equation as y=-4 and plots this.

    Again, the function f(x) must be specified before it can be sketched.
     
  10. Mar 29, 2007 #9
    Exactly. But, since he didn't specify what f(x) is, I took it as 0 as well and ended up with y = -4. Wouldn't that work then?
     
  11. Mar 29, 2007 #10

    cristo

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    If f(x)=0, then y=f(x)-4 will become y=-4, but why are you taking f(x)=0? Why not take f(x)=17x, or f(x)=x^9? The function f(x) must be specified before the graph can be drawn.
     
  12. Mar 29, 2007 #11
    I'm taking it as a 0 because he didn't specify any other number. If he had specified 1, 2, 3, 4 etc. then I have would've used that. When I was doing this in my homework, an exact question I came upon was y = f(x) - 6 and we had to assume that f(x) = 0 since f(x) wasn't defined.

    It's like taking this equation: x^2 + 4x - 5. It's the same as: (1)^2 + 4(1) - 5 because x isn't defined so we take it for 1. Right? At least that's how I learned it.
     
  13. Mar 29, 2007 #12

    cristo

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    f(x) isn't a number, it's a function. If you evaluate it at a certain value of x, then it will have a numerical value, but before you do that, it is a function!

    Like I said earlier; there is no reason to assume f(x)=0, just because the OP has not told us what it is!

    I don't really know what you're doing here. It seems that you are evaluating the function at the point x=1.

    We definitely need to know the value of the function before we can sketch the graph (wow, how many times have I said that in this thread? :rolleyes: )
     
  14. Mar 29, 2007 #13
    Yes, I know it's a function. Maybe the way we learned things is different.

    Also, for the 2nd part, if you had to say what x was without it being defined at all, what would you say? As far as I know, when it's only a variable (be it x, a, b etc.), we take it as 1.
     
  15. Mar 29, 2007 #14

    cristo

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    I'd say it was x. If you're not told the value of x at which to evaluate the function, then you cannot just pick anything!
    I'm sure that you're confusing things here. You probably took x=1 when you were required to evalute the function at x=1; i.e. you wanted f(1)
     
  16. Mar 29, 2007 #15
    I was speaking in general and not keeping f(x) in mind regarding the variables being 1. What I'm trying to say is consider this equation: x + 5. If we were to re-write that in another way, it can be 1x + 5. x isn't defined with 1, what I meant to say is explained in that equation. Maybe I said it wrong. Off to bed now; school tomorrow.
     
    Last edited: Mar 29, 2007
  17. Mar 29, 2007 #16
    thanks for your help!
     
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