### Home > CALC > Chapter 1 > Lesson 1.1.1 > Problem 1-10

For each function

*f*(*x*) sketched below, sketch*f*(−*x*) and compare it with*f*(*x*). Then describe its symmetry. Homework Help ✎EVEN AND ODD FUNCTIONS--INFORMALLY

A function that is symmetric with respect to the*y*-axis, like that in part (a) above, is called an**even**function. A function that is symmetric with respect to the origin, such as that in part (b), is called an**odd**function.

Sketch examples of even and odd functions. Include how you can test whether a function is even or odd. Then list some famous even/odd functions from your parent graphs, and the symmetries associated with even and odd functions.

What does*f*(−*x*) mean?

Compare *f*(1) and *f*(−1)

Compare *f*(2) and *f*(−2)

keep going... *f*(3) and *f*(−3)

The sketch of *f*(−*x*) should be identical to the given graph *f*(*x*).

On this graph, *f*(−*x*) = −*f*(*x*).

Plot all negative *y*-values in the positive region, and plot all positive *y*-values in the negative region.

Even functions are symmetrical ACROSS the *y*-axis, they have reflective symmetry. Odd functions are symmetrical ABOUT the origin, they have 180° rotational symmetry.

Graph (a) is even. Graph (b) is odd.

Famous even functions include: *y* = *x*^{2}, *y* = *x*^{4}, *y* = cos*x*, and all vertical translations and stretches of the graphs above.

Famous odd functions include: *y* = *x*, *y* = *x*^{3}, *y* = sin*x*, and all stretches of the graphs above.