• Relation: a relationship between sets of info
– Pairing of names and heights of Precalc students
– Data for times and high tides for Hampton VA
• Domain: possible values of inputs (typically called “x”)
• Range: possible values of outputs (typically called “y”)
• Function: a “well-behaved” type of relation
– Each input has one and only one output!
Which is a function?
Name of function
(“f of x”)
f(x) = 5x2 +3
Rule, or directions that tell
you what to do with the input
to produce the output
(“square it, multiply it by 5,
then add 3 to it”)
• Unless told otherwise, domain of f is all real
number inputs that the rule produces a real
• Two primary restrictions
– Can’t divide by zero
– Can’t take the square root of a negative number
• Some real-world problems may further restrict
– Does negative time or distance make sense?
• The rule includes several formulas
• Each formula applies to certain values of the
• So which rule or formula you apply depends
on the input value
• What is f(-5)? f(8)? the domain of f?
2x +3 if x < 4
x2- 1 if 4 ≤ x ≤ 10
Greatest Integer Function
• For any number x, round down to the nearest
integer less than or equal to x
• The symbol is a set of brackets
• Remember negative numbers round down,
which is left on the number line!
• This is an example of a step function
• TI-83/4: MATH, NUM, 5: int(
• What is f(-4.7)? f(-3)? f(0)? f(5/4)? f(π)?
f(x) = [x]