### Home > CALC > Chapter 1 > Lesson 1.4.1 > Problem1-138

1-138.

Given a portion of the graph of $f(x)$ at right: .

1. Sketch the rest of $f(x)$ if $f(x)$ is even and find $A(f, -3 ≤ x ≤ 3)$.

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

2. Sketch the rest of $f(x)$ if $f(x)$ is odd and find $A(f, -3 ≤ x ≤ 3)$.

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

Because of the symmetry of the areas, $A(f, -3 ≤ x ≤ 3) = 0$.

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