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

Name Date

WORKSHEET 8.3: FINDING THE RANGE OF A FUNCTION

-------------------------------------------------------------------------------------

You can find the range of a function if you are given members of the domain. Follow the steps

below:

1. If the function is expressed in arrow notation, rewrite the function as an equation.


2. Substitute a member of the domain forx. Evaluate the expression to find the value of
   the function that is paired with the member of the domain. (Continue substituting until
   you have found the values of the function that are paired with every value ofx.)


3. Rewrite the values of the function in braces. This represents the range of the function
   with the given domain.

EXAMPLE

Find the range.D={−1, 1, 2} h:x→x^2 +x or h(x)=x^2 +x

h(−1)=(−1)^2 +(−1)= 0 h(1)= 12 + 1 = 2 h(2)= 22 + 2 = 6 R={0, 2, 6}

DIRECTIONS: Find the range of each function.

1. h:x→ 7 x;D={−3, 4, 5} 2. I(x)= 3 x^2 ;D={−1, 1, 2}


2. j(x)=

√

x+4;D={−4, 0, 5} 4. F(x)→|x− 5 |;D={0, 1, 5}

5. g(x)=x^2 − 3 x;D={−1, 0, 3} 6. f:x→

1

x− 1

;D={−1, 0, 2}

CHALLENGE:Salvatore said that the range off(x)=x^2 + 2 x+4withthe

domain of{−3,−2,−1, 0}was{7, 4, 3}. Michelle said he was wrong

because there are four members of the domain and there must be four

members of the range. Who is correct? Explain your answer.

279

Copyright

©

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