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Math Help - Basic transforming functions help

  1. #1
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    Basic transforming functions help

    Hello,

    I'm looking for a bit of help on something that should be pretty easy, but I'm not quite understanding how to go about this.

    The assignment question is as follows:

    For the function y = f(x) graphed below. Sketch each function on the grid provided.
    For each graph: a) explain what changes you made to y = f(x)
    b) Give the new coordinates of the point provided in each question.



    The question then is to transform the graph to y = f(1/2x), the point given to me to give the new coordinates for is (4, 2).

    Maybe I'm missing something here but wouldn't I have to have the actual function of the graph given to me before I can transform it? Or should I be able to do it with just a sketch of the original function?

    Thanks for any help, I'm doing an online class thats the equivalent of high school level stuff but it's been a few years since I've done any math courses so I am even having trouble with the basics!
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  2. #2
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    Re: Basic transforming functions help

    I'm going to assume you mean y= f((1/2)x), not y= f(1/(2x)).
    The "x" their is unchanged- it is only the y value that is changed.

    In (4, 2), x= 4 so (1/2)x= (1/2)4= 2. That is, y= f(2). And your graph shows the point (2, -2) which tells us that f(2)= -2. That is, starting with x= 4, we arrive at y= -2. The point (4, 2) is transformed to the point (4, -2).
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  3. #3
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    Re: Basic transforming functions help

    Thanks, I solved the rest of my problem and that helped.

    I have two other questions though, still related to the topic of this thread so I'll just ask them here as well.

    On a TI-83/84, what syntax is suppose to be used to do a horizontal translation on a linear function? Every other type of function seems to have no problem with this. For example, if I type in y=sqrt(x-4) or y=abs(x-4) it will translate the graph 4 units right. However, if I type in y=(x-4) with regular brackets it will treat it as a vertically translation and move the graph 4 units down. Wolfram does this too. What syntax am I suppose to use to get the calculator or Wolfram to recognize a horizontal translation on a simply linear function?

    Also, if I have the function y=2(x-2), will this translate the function 2 units right, or 4 units right? In other words, does the horizontal translation apply before the contents of the brackets are multiplied by the coefficient, or after?

    Thanks!
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  4. #4
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    Re: Basic transforming functions help

    Quote Originally Posted by TypicalNinja View Post
    Thanks, I solved the rest of my problem and that helped.

    I have two other questions though, still related to the topic of this thread so I'll just ask them here as well.

    On a TI-83/84, what syntax is suppose to be used to do a horizontal translation on a linear function? Every other type of function seems to have no problem with this. For example, if I type in y=sqrt(x-4) or y=abs(x-4) it will translate the graph 4 units right. However, if I type in y=(x-4) with regular brackets it will treat it as a vertically translation and move the graph 4 units down. Wolfram does this too. What syntax am I suppose to use to get the calculator or Wolfram to recognize a horizontal translation on a simply linear function?

    Also, if I have the function y=2(x-2), will this translate the function 2 units right, or 4 units right? In other words, does the horizontal translation apply before the contents of the brackets are multiplied by the coefficient, or after?

    Thanks!
    I think you'll find y = x - 4 is a translation BOTH 4 units down and 4 units right. Can you see why?
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