What is the function of this graph

Question

The graph shows something similar to f(x)=sqrt(absolute-value(4-x^2)) but the lines that extrude from the x axis after the ends of the semicircle are straight reather than curved.

To further explain, The function starts with a line which has a slope of -1 from -infinity till -2 then a semicircle from -2 till 2 than a line with slope 1 starts from 2 till infinity.

 

Does this graph have an equation, not being a peicewise function.

Answer 1

you describe the graph fairly well but do not give enough information to specify the y values (there are many lines on the interval (-infinity,-2) having slope -1, for example). on second thought, I believe that you answer this question (of mine) by your use of the unusual word extrude! So let's assume that the x-intercepts are ±2 and the function is continuous; then all is clear except for the semicircle...is it the upper half of a circle, or the lower half?

 

Grammar/spelling observations: rather   piecewise.

Yes, it looks like a piecewise definition is required for this function.