Objectives
Basic Functions
and Their Graphs
• Find the domain & range of a relation.
• Determine whether a relation is a function.
• Determine if an equation represents a
function.
• Evaluate a function.
What Is A Function?
Domain & Range
EXAMPLE
• A relation is a set of ordered pairs.
• Domain: first components in the relation
(independent)
• Range: second components in the relation
(dependent, the value depends on what
the domain value is)
• Functions are SPECIAL relations: A
domain element corresponds to exactly
ONE range element.
• Consider the function: eye color
• (Assume all people have only one color,
and it is not changeable)
• It IS a function because when asked the
eye color of each person, there is only one
answer.
• i.e. {(Joe, brown), (Mo, blue), (Mary,
green), (Ava, brown), (Natalie, blue)}
• NOTE: the range values are not
necessarily unique.
Examples
Determine whether each relation is a function.
Give the domain and range of each.
How do you determine if an
Equation represents a Function?
• If an equation is solved for y and more
than one value of y can be obtained for a
given x, then the equation does not define
y as a function of x.
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Example
Example
• Determine whether the equation defines y
as a function of x.
• Determine whether the equation defines y
as a function of x.
Evaluating a function
Example
• Common notation: f(x) = function
• Evaluate the function for the given values.
• Evaluate the function at various values of x,
represented as: f(a), f(b), etc.
• Example:
f(x) = 3x – 7
f(2) = 3(2) – 7 = 6 – 7 = -1
f(3 – x) = 3(3 – x) – 7 = 9 – 3x – 7 = 2 – 3x
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