Which of these is an odd function?

Question 11 options:

f(x) =3x2+7

f(x) =2x3+x

f(x) =5x2−6

f(x) =4x3+2x2

Step-by-step explanation:

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

So the only odd function on the list!

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step-by-step explanation: