Answer:
Step-by-step explanation:
An odd function <em>f</em> is one where . We can interpret this is meaning: reflecting the graph horizontally
has the same effect as reflecting it vertically
. The only graphs that meet this requirement are ones with reflectional symmetry across the line y = x, so we can immediately elimate the functions
and
, which have horizontal symmetry, but not the kind of symmetry we're looking for.
That leaves us with and
. One feature of exponents we can utilize is that -1 to an even power is 1, while -1 to an odd power is -1. If we want
, we need to flip the signs of <em>all </em>the coefficients, and we can only do that if all the powers of x are odd. The only function with only odd powers of x is
, and plugging in -x to the function reveals that
So the only odd function on the list!
