Products and Quotients of Functions

Products and Quotients of Functions

Even vs. Odd functions:

Even Functions – f(x) = f(-x) for all values of x in the domain. It is symmetrical about the y-axis.

Ex.

Odd Functions – f(x) = -f(x) for all x in the domain. Odd functions are rotationally symmetrical about the origin.

Ex. y=x

Ex. Let f(x) = x, , , and .

ODD EVEN ODD EVEN

Note:

Note the following characteristics of even and odd functions:

Product / Symmetry of Factors / Symmetry of Product
/ ODD x EVEN
/ ODD x ODD
/ ODD x ODD
/ EVEN x EVEN
/ ODD x EVEN x EVEN

Rules of multiplying even and odd functions

i)  When you multiply two even functions you get an even function

ii)  When you multiply two odd functions, you get an even function

iii)  When you multiply an odd and an even function, you get an odd function.

Ex.2. Let f(x) = x + 3 and , sketch a graph for the following combined functions, and state the domain and range of each.

a. b.

Key points from the Lesson:

a.  A combined function represents the product of the two functions f(x) and g(x).

b. is the quotient of f(x) and g(x), g(x)0.

c. The domain of a product is the domain common to the components. The domain of a quotient is restricted by any values that make the denominator of the quotient equal to zero.