What doesf(−x) mean?
Compare f(1) and f(−1)
Compare f(2) and f(−2)
keep going... f(3) and f(−3)
The sketch of f(−x) should be identical to the given graph f(x).
On this graph, f(−x) = −f(x).
Plot all negative y-values in the positive region, and plot all positive y-values in the negative region.
Even functions are symmetrical ACROSS the y-axis, they have reflective symmetry. Odd functions are symmetrical ABOUT the origin, they have 180° rotational symmetry.
Graph (a) is even. Graph (b) is odd.
Famous even functions include: y = x2, y = x4, y = cosx, and all vertical translations and stretches of the graphs above.
Famous odd functions include: y = x, y = x3, y = sinx, and all stretches of the graphs above.