### Home > CALC > Chapter 2 > Lesson 2.1.1 > Problem 2-12

2-12.

Compare whether each function below is an even function, an odd function, or neither. Homework Help ✎

*f*(*x*) =*x*^{2}*f*(*x*) =*x*^{3}*f*(*x*) = 2^{x}*f*(*x*) = sin*x*

Definition of an even function: *f*(*a*) = *f*(−*a*)

Definition of an odd function: *f*(−*a*) = −*f*(*a*)

*f*(*x*) = *x*² *f*(*a*) = (*a*)²= *a*² *f*(−*a*) = (−*a*)²= *a*².......... *f*(*a*) = *f*(−*a*) it's even!

−*f*(*a*) = −(*a*)²= −*a*².............*f*(−*a*) ≠ −*f*(*a*) it's NOT odd.

Refer to hint and steps in part (a).

Refer to hint and steps in part (a).

Even functions are symmetrical over the *y*-axis.

Odd functions are symmetrical about the origin.

Sketch a graph of sin*x* and describe the symmetry.