Half-Ellipse Function
Function defined by a relation in the form f(x) = [latex]\frac{b}{a}[/latex] [latex]\sqrt{{a}^{2}~ – {x}^{2}}[/latex] or f(x) = − [latex]\frac{b}{a}[/latex] [latex]\sqrt{{a}^{2}~ – {x}^{2}}[/latex] where a is the horizontal half-axis and b is the vertical half-axis of an ellipse centered on the origin point.
Examples
Here is a graph of a function defined by the f(x) = [latex]\dfrac{1}{3}[/latex] [latex]\sqrt{{9}~ – {x}^{2}}[/latex] :
Here is a graph of the function defined by the relation f(x) = − [latex]\dfrac{1}{3}[/latex] [latex]\sqrt{{9}~ – {x}^{2}}[/latex] :
