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Function Notation and Interval
Notation
Vocabulary: function, function notation, evaluate, set
notation, interval notation
Objectives:
I understand function notation and know what it
means to evaluate a function.
I can find the sum, difference, product, and quotient
of two functions
I can convert from set notation to interval notation
and vice versa
What is a function?
A relation in which each x-value
(independent variable) has exactly one y-
value (dependent variable).
Each input has exactly one output.
X’s can’t repeat, y’s can repeat.
What is the vertical line test?
Used to tell if a graph is a function
If any vertical line intersects a graph in
more than one point, then it is not a
function.
What does it mean to evaluate
a function?
To find the value at a given input value.
Example: If f(x) = x2 + 3x + 5, evaluate each of the
following
a) f(2)
b) f(-4)
c) f(-x)
Combining Functions
If f and g are functions, then…
𝑓 + 𝑔 𝑥 = 𝑓 𝑥 + 𝑔 𝑥
𝑓 − 𝑔 𝑥 = 𝑓 𝑥 − 𝑔 𝑥
𝑓 ∙ 𝑔 𝑥 = 𝑓 𝑥 ∙ 𝑔 𝑥
𝑓
𝑔𝑥 =
𝑓(𝑥)
𝑔(𝑥)