http://www.ck12.org Chapter 1. Functions and Graphs
power will never produce a negative number or zero. The restriction can be observed in the graph by the way the log
function approaches the vertical linex=0 and shoots down to infinity.
- The reciprocal function:y=^1 x
Domain Restriction:x 6 = 0
The reciprocal function is restricted because you cannot divide numbers by zero. Anyxvalues that make the
denominator of a function zero are outside of the domain. This restriction can be observed in the graph by the way
the reciprocal function never touches the vertical linex=0.
Rangeis the possible outputs of a function. Just about any function can produce any output through the use of
transformations and so determining the range of a function is significantly less procedural than determining the
domain. Use what you know about the shape of each function and their equations to decide whichyvalues are
possible to produce and whichyvalues are impossible to produce.
Example A
Domain and range are described in interval notation. Convert the following descriptions of numbers into interval
notation.
a. All numbers.
b. All negative numbers not including 0.
c. All positive numbers including 0.
d. Every number between 1 and 4 including 1 and 4.
e. Every number between 5 and 6 not including 5 or 6.
f. The numbers 1 through 2 including 1 but not including 2 and the numbers 10 through 25 including both 10
and 25.Solution:Parentheses, ( ), mean non-inclusive. Brackets, [], mean inclusive.
a.(−∞,∞)Note: Parentheses are always used with infinity.