CK-12-Pre-Calculus Concepts

1.4. Domain and Range http://www.ck12.org

Guided Practice

1. Identify the domain and range of the following function written in a table:

TABLE1.5:

x y

0 5

1 6

2 7

(^126)
π π 2

2. Identify the domain of the following three transformed functions.
   a.y= 10

√

2 −x− 3

b.y=x (^2) + 73 xx+ 12
c.y=−4 ln( 3 x− 9 )+ 11

3. What is the domain and range of the sine wave?
   Answers:


4. The specific equation of the function may be hidden, but from the table you can determine the domain and range
   directly from thexandyvalues. It may be tempting to guess that other values could potentially work in the table,
   especially if the pattern is obvious, but this is not the kind of question that asks what the function could be. Instead
   this question just asks what is the stated domain and range.
   Domain:x∈{ 0 , 1 , 2 ,^12 ,π}
   Range:y∈{ 5 , 6 , 7 ,π 2 }
   Note that the two 6’s that appear in the table do not need to be written twice in the range.


5. Each of the functions requires knowledge of one of the three domain restrictions.
   a.y= 10 √ 2 −x− 3
   The argument of the function must be greater than or equal to 0.

2 −x≥ 0

−x≥− 2

x≤ 2

Domain:x∈(−∞, 2 ]

b.y=x (^2) + 73 xx+ 12
The denominator cannot be equal to 0. First find what values ofxwould make it equal to zero and then you can
exclude those values.
x^2 + 7 x+ 12 = 0
(x+ 4 )(x+ 3 ) = 0
x=− 4 ,− 3