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

Name Date

WORKSHEET 8.2: FINDING THE DOMAIN OF A FUNCTION

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The domain of a function is the values ofxfor which the function is defined. The domains of

most functions are all real numbers unless there are restrictions on the variable. Use the

steps below to find restrictions on the variable:

1. If the variable is written within the square root symbol, write and solve the inequality
   that states the radicand must be greater than or equal to 0. This is the domain of the
   function.


2. If the variable is in the denominator, write and solve the inequality that states the
   denominator is not equal to 0. The domain is all real numbers except that value.


3. If the square root symbol is in the denominator, write and solve the inequality that
   states the radicand must be greater than 0. This is the domain of the function.

EXAMPLES

f(x)= 3 x^2 There are no restrictions onx. The domain is all real numbers.

g(x)=

1

x− 10

x− 10 = 0 →x= 10 The domain is all real numbers except 10.

DIRECTIONS: Find the domain of each function.

1. h(x)=x− 5 2. I(x)=

√

x− 7

3. g(x)=

1

x+ 4

4. j(x)=

1

2

√

x+ 8

5. f(x)=x^2 + 1 6. k(x)=|x− 3 |+ 1


6. h(x)=x^3 − 2 8. I(x)=

1

2 x+ 4

CHALLENGE:Evie said that the domain off(x)=

1

√

x− 1

comprises all real

numbers greater than or equal to 1. Do you agree? Explain your reasoning.

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2011 by Judith A. Muschla, Gary Robert Muschla, and Erin Muschla. All rights reserved.