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  1. MHB Craftsman

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    #1
    Data

    A graph in the form of $y=(x-1)^2-6$

    Problem

    Write down the equation of the function corresponding to the graph obtained when the above graph is translated 1 unit in the negative direction of the $x$ axis

    Workings:

    -

    Where do I need help

    In writing the equation of the funtion.

  2. Pessimist Singularitarian
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    #2
    If we are given a function $f(x)$, then to translate the graph of that function $k$ units to the left, we may use $f(x+k)$.

    Can you proceed?

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    #3 Thread Author
    Quote Originally Posted by MarkFL View Post
    If we are given a function $f(x)$, then to translate the graph of that function $k$ units to the left, we may use $f(x+k)$.

    Can you proceed?
    $\displaystyle f(x)=a(x-h)^2+k$

    The function is in this form.

    Substituting the values,

    $y=(x-1)^2-6$

    k=-6

    Is it $f(x-6)$? but I am not sure whether this is correct?

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    #4
    You are given:

    $ \displaystyle y(x)=(x-1)^2-6$

    So, to translate this one unit to the left, use:

    $ \displaystyle y(x+1)=((x+1)-1)^2-6=x^2-6$

  5. MHB Craftsman

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    #5 Thread Author
    Quote Originally Posted by MarkFL View Post
    You are given:

    $ \displaystyle y(x)=(x-1)^2-6$

    So, to translate this one unit to the left, use:

    $ \displaystyle y(x+1)=((x+1)-1)^2-6=x^2-6$
    Thank you very much , Now I see it in desmos



    Quote Originally Posted by MarkFL View Post
    If we are given a function $f(x)$, then to translate the graph of that function $k$ units to the left, we may use $f(x+k)$.

    Can you proceed?
    But what I don't still understand is it's derivation.

    Now what has actually happened here $ \displaystyle y(x+1)=((x+1)-1)^2-6=x^2-6$;

    Using $f(x+k)$ Do you plug in the values for $f,x,k$ from the given function.

    What does $f$ stand for & from which part of the function was a value taken.

    A comment here would be highly appreciated
    Last edited by mathlearn; September 17th, 2016 at 01:32.

  6. Pessimist Singularitarian
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    #6
    Suppose we are given a function $f(x)$ and we wish to shift the graph of that function horizontally. If we wish to shift the function to the left $k$ units, then we can think of accomplishing this by moving our coordinate axes horizontally to the right $k$ units, that is:

    $ \displaystyle X=x+k$

    So now what we have is that:

    $ \displaystyle f(X)=f(x+k)$

    is the graph of $f(x)$ shifted to the left by $k$ units. Now, in this problem, we are given the function:

    $ \displaystyle y(x)=(x-1)^2-6$

    And we are told to shift it 1 unit to the left.

    So, in terms of what I posted above, we have $y=f,\,k=1$ and so there results:

    $ \displaystyle y(x+1)=((x+1)-1)^2-6=x^2-6$

  7. MHB Craftsman

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    #7 Thread Author
    Quote Originally Posted by MarkFL View Post
    Suppose we are given a function $f(x)$ and we wish to shift the graph of that function horizontally. If we wish to shift the function to the left $k$ units, then we can think of accomplishing this by moving our coordinate axes horizontally to the right $k$ units, that is:

    $ \displaystyle X=x+k$

    So now what we have is that:

    $ \displaystyle f(X)=f(x+k)$

    is the graph of $f(x)$ shifted to the left by $k$ units. Now, in this problem, we are given the function:

    $ \displaystyle y(x)=(x-1)^2-6$

    And we are told to shift it 1 unit to the left.

    So, in terms of what I posted above, we have $y=f,\,k=1$ and so there results:

    $ \displaystyle y(x+1)=((x+1)-1)^2-6=x^2-6$
    Thank you very much again

    To shift the function to the left y(x+1) and vice versa to shift the function right y(x-1)

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