(a) Classify the following functions as odd, even or neither
\[ \begin{align}
f(x) &= \frac{1}{x^2} \\
f(x) &= 1 + |x^2-3| \\
f(x) &= \cos |x| \\
f(x) &= \frac{1}{1 - x^2} \\
f(x) &= \frac{1}{\sqrt{1 + x^2}} \\
\end{align} \ \]
(b) Explain how oddness and evenness can help to sketch a function.
For each of the example functions in the lesson, determine how the graph would change if
(a) f(x) was translated right 2 units.
(b) f(x) was reflected in the x-axis.
(c) f(x) was translated 2 units in the positive y direction.