# Thread: Formula for a function

1. ## Formula for a function

"Find a formula that describes the following function, which is composed of straight lines and a semicircle"

So far all I know is the equation has (x-1)(x+1), intersects at 1 and -1, but I don't get how the circle and straight lines kick in. Do I have to use some sort of hybrid between a straight line equation and the circle equation?
(x - h)2 + (y - k)2 = r2

2. Originally Posted by arkhampatient

"Find a formula that describes the following function, which is composed of straight lines and a semicircle"

So far all I know is the equation has (x-1)(x+1), intersects at 1 and -1, but I don't get how the circle and straight lines kick in. Do I have to use some sort of hybrid between a straight line equation and the circle equation?
(x - h)2 + (y - k)2 = r2

It is a hybrid function. The equations of the two lines cannot be uniquely found fro the given information.

The equation of the circle can be found since you know the radius and the coordinates of the centre.

3. $\displaystyle \frac{1-sgn(x+1)}{2}(-x-1)+\frac{1-sgn(|x|-1)}{2}\sqrt{1-x^2}+\frac{1+sgn(x-1)}{2}(-x+1)$

4. $\displaystyle f(x) = \left\{ {\begin{array}{rl} {m\left( {\frac{{\left| x \right|}} {x} - x} \right),} & {\left| x \right| > 1\;\& \,m > 0} \\ {\sqrt {1 - x^2 } ,} & {\left| x \right| \leqslant 1} \\ \end{array} } \right.$