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1-138.

A portion of the graph of $y = f(x)$ is given at right: 1-138 HW eTool (Desmos). Homework Help ✎

1. Sketch the rest of the graph if $f$ is even and calculate the area under the curve for $−3 ≤ x ≤ 3$.

If a function is even, it is symmetric about the $y$-axis.

2. Sketch the rest of the graph if $f$ is odd and calculate the area under the curve for $−3 ≤ x ≤ 3$.

If a function is odd, it also has $180º$ rotational symmetry about the origin.

Use the eTool below to visualize this problem.
Click the link at right for the full version of the eTool: Calc 1-138 HW eTool