Easy Algebra Step-by-Step

196 Easy Algebra Step-by-Step

Step 2. Isolate the fi rst and second coordinates of the

function f.

The domain of f is D = {2, 3, 4, 5} and the range

of f is R= {1, 5, 7}.

Problem Identify the domain and range of the function g= {(1, 2), (2, 3),

(3, 4), (4, 5), ...}.

Solution

Step 1. Isolate the fi rst and second coordinates of g.

The domain of g is D= {1, 2, 3, 4, ...}, and the range of g is R=

{2, 3, 4, 5, ...}.

Form 2: Equation or Rule

The ordered pair form is very useful for getting across the basic idea, but

other forms are more useful for algebraic work.

A function is a rule of correspondence between two sets A and B such

that each element in set A is paired with exactly one element in set B. In

algebra, the rule is normally an equation in two variables. An example is the

equation y= 3 x+ 7. For t h is rule, 1 is paired with 10, 2 with 13, and 5 with

22. This is equivalent to saying that the ordered pairs (1, 10), (2, 13) and
    (5, 22) are in the function.
    If the domain of a function is not obvious (as it is in the fi rst two prob-
    lems) or not specifi ed, then it is generally assumed that the domain is the
    largest set of real numbers for which the equation has numerical meaning
    in the set of real numbers. The domain, then, unless otherwise stated, is all
    the real numbers except excluded values. To deter-
    mine the domain, start with the real numbers and
    exclude all values for x, if any, that would make the
    equation undefi ned over the real numbers.

Problem State the domain of the given function.

a. y

x

=

−

3

1

b. yxx−^25 +

Suggestion: When listing the

elements of the domain and

range of a function, put the

elements in numerical order.

Routinely, division by 0 and even

roots of negative numbers create

domain problems.