Piecewise Linear Function

A piecewise function is a function that is given by different expressions on different intervals. The graph of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(x) = \begin{cases} x^2, & \mbox{if}\ x< 2 \\ - \left(x - 3\right)^2 +9, & \mbox{if}\ x\ge2 \end{cases}} is shown on the right. The open circle indicates that the point is not included on the graph and the closed circle indicates that the point is included on the graph. So Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle f(2)} = 8 not 4.

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle \lim_{x\to\infty} }