Section 1.2

A graph has symmetry with respect to the y-axis if whenever (x,y) is on the graph, so is the point (-x,y). A graph has symmetry with respect to the origin if whenever (x,y) is on the graph, so is the point (-x,-y). A graph has symmetry with respect to the x-axis if whenever (x,y) is on the graph, so is the point (x,-y).

A function whose graph is symmetric with respect to the y-axis is an EVEN function.
A function f is EVEN if, for each x in the domain of f, f(-x) = f(x)

A function whose graph is symmetric with respect to the origin is an ODD function.
A function f is ODD if, for each x in the domain of f, f(-x) = -f(x)

Here is a practice problem that can be found on page 95 in the book.
a. g(x) = x^3 - x
Is this function even, odd, or neither?
g(x) = x^3 - x =
g(-x) = (-x)^3 - (-x) =
-x^3 + x =
-(x^3 - x) =
-g(x)
This function is odd because f(-x) = -f(x)