CONFUSING FUNCTION QUESTION

[texas07]

Find an expression for the function whose graph consists of the line segment from the point (-2, 2) to the point (-1,0) together with the top half of the circle with the center the origin and the radius 1.

Is there a formula to solve this problem? Like a linear function? And does this mean that the origin of the circle is at 1 or (0,0) ? The wording of it threw me off but that is exactly how it is written in my book.

 

[galactus]

It would appear they want you to build a piecewise function.

Find the equation of the line that passes through (-2,1), (-1,0)

What is the equation of the upper semi-circle with radius 1?. The circle has origin at (0,0)

\(\displaystyle f(x)=\left\{\begin{array}{cc}\text{line equation}, \;\ -2\leq x\leq -1\\ \text{circle equation}, \;\ -1< x\leq 1\end{array}\)

This is one way. The inequalities determine rather or not the point is a closed or open interval.