1. ## 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

2. Originally Posted by Sosi
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

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

To determine the value of $a$. find any points of intersection...

3. 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 - )

4. Originally Posted by Sosi
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.