An odd function f 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 all 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
Plzz ! if you were constructing a triangular frame, and you had wood in the length of 4 inches, 4 inches, and 7 inches, would it make a triangle? would you be able to create a frame from these pieces of wood? yes or no? = explain your mathematical thinking/show your work: