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3-78.

Graph the following piecewise-defined function. 3-78 HW eTool (Desmos). Homework Help ✎

$y = \left\{ \begin{array} { l l } { x ^ { 3 } + 3 } & { x \leq 0 } \\ { | x | + 3 } & { x > 0 } \end{array} \right.$

Draw a vertical line at $x = 0$.
Graph the top function then erase everything to the left of the vertical line.
Graph the bottom function then erase everything to the right of the vertical line.

1. Now shift the function down 3 units and to the left 2 units and then draw the new graph on the same set of axes.

2. Write a new set of equations for the shifted piecewise-defined function.

Use the eTool below to graph the shifted function on the same set of axes as the original graph.
Click the link at right for the full eTool version: INT3 3-78 HW eTool