The Algebra Teacher\'s Guide to Reteaching Essential Concepts and Skills

Teaching Notes 8.2: Finding the Domain of a Function

The rule, domain, and range are three components of functions. Students may assume that

functions are defined for all these values and not realize that sometimes some values of functions

are undefined.

1. Explain that all functions have a domain, range, and a rule that assigns to each member of
   the domain exactly one member of the range.


2. Review some common functions and their associated equations: linear,f(x)=x;squar-
   ing,g(x)=x^2 ;cubing,h(x)=x^3 ; and absolute value,I(x)=|x|. Sketch each graph using a
   t-table or calculator for your students. Using the equation and the graph, point out that for
   every value ofxthere is exactly one value fory. Also note that the domain of these functions
   is all real numbers.


3. Explain the square root function,f(x)=

√

x,andsketchthegraph.Notethatxmust be

greater than or equal to 0, otherwisef(x) has no meaning.

4. Presenth(x)=

1

√

x

and sketch the graph. Note thatxmust be greater than 0 becauseh(x)is

not defined whenxis less than or equal to 0.

5. Review the information and the examples on the worksheet with your students. Emphasize
   the steps for finding restrictions on the variable. If necessary, review the steps for solving
   the equations in detail.

EXTRA HELP:

If the function is defined for all real numbers, the domain of the function is all real numbers.

ANSWER KEY:

(1)Allrealnumbers (2)All real numbers greater than or equal to 7

(3)All real numbers except− 4 (4)All real numbers greater than− 8

(5)Allrealnumbers (6)All real numbers

(7)Allrealnumbers (8)All real numbers except− 2

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(Challenge)Evie is incorrect. The domain off(x) is all real numbers greater than 1.

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276 THE ALGEBRA TEACHER’S GUIDE