Teaching Notes 8.3: Finding the Range of a Function
The members of the range of a function are they-values of the function. Many students find
function notation confusing and they often fail to make the correct substitutions when they try
to find the range of a function.- Discuss the meaning of a function: A function consists of a domain, range, and a rule that
assigns to each value ofxexactly one value ofy. Explain that the rule may be expressed as an
equation or with arrow notation. - Offer some examples of functions, which are defined by an equation such as the absolute
value function,f(x)=|x|; the square root function,g(x)=
√
x; and the reciprocal function,
F(x)=1
x. Show your students how each can be written using arrow notation:f:x→|x|,g:
x→√
x,andF:x→1
x. Explain how to interpret the notation.fpairsxwith its absolute
value;gpairsxwith its square root; andFpairsxwith its reciprocal.
3. Explain that the range of a function can be determined by substituting each member of the
domain in the equation.
4. Review the information and example on the worksheet with your students. In the example,
be sure that your students understand that ‘‘D’’ stands for domain and ‘‘R’’ stands for range.
EXTRA HELP:
When a member of the range is paired with two different members of the domain, write the
member of the range only once.ANSWER KEY:
(1){−21, 28, 35} (2){3, 12} (3){0, 2, 3} (4){5, 4, 0} (5){4, 0} (6){
−
1
2
,−1, 1
}
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(Challenge)Salvatore is correct.f(−3)=7;f(−2)=4;f(−1)=3;f(0)=4. The range is
{7, 4, 3}. Each member of the range should be written only once.
------------------------------------------------------------------------------------------278 THE ALGEBRA TEACHER’S GUIDE