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Math Help - Quadratic & Linear Function problem

  1. #1
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    Quadratic & Linear Function problem

    Hello!

    I have a more complex problem but for simplifications purposes I will explain it in simpler terms:

    I have a function which I know its behaviour:

    y= x^2 (IF x<a) OR y=x (IF x>a).

    Note that this is a single, continuum function. I have 2 problems in here:

    1. I dont know how to write this down in an analytical formula. I want a general formula that gives me the expression of y and includes the conditions that if x<a or x>a;

    2. What I want to plot is the crossover from the quadratic regime to the linear regime. That is, i want an analytical formula that gives me the expression of the crossover.


    Could I have some help please? All tips are welcomed!
    Many thanks
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  2. #2
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Sosi View Post
    Hello!

    I have a more complex problem but for simplifications purposes I will explain it in simpler terms:

    I have a function which I know its behaviour:

    y= x^2 (IF x<a) OR y=x (IF x>a).

    Note that this is a single, continuum function. I have 2 problems in here:

    1. I dont know how to write this down in an analytical formula. I want a general formula that gives me the expression of y and includes the conditions that if x<a or x>a;

    2. What I want to plot is the crossover from the quadratic regime to the linear regime. That is, i want an analytical formula that gives me the expression of the crossover.


    Could I have some help please? All tips are welcomed!
    Many thanks
    What you have is

    f(x)=\left\{\begin{array}{cc}x^2,&\mbox{ if }<br />
x\leq a\\x, & \mbox{ if } x>a\end{array}\right..

    To determine the value of a. find any points of intersection...
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  3. #3
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    do you think there is any way of writing down the formula of y without using \left\{\ ? I mean, a more regular way with only the basic operational symbols ( *, /, + or - )
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  4. #4
    No one in Particular VonNemo19's Avatar
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    Quote Originally Posted by Sosi View Post
    do you think there is any way of writing down the formula of y without using \left\{\ ? I mean, a more regular way with only the basic operational symbols ( *, /, + or - )
    No. this is a piecewise defined function by its very nature.
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