Function Notation and Interval Notation and... · notation, interval notation Objectives: I understand function notation and know what it means to evaluate a function.

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.

Function notation: f(x)

“f of x” or “f at x”

Represents the value of a function

at the number x

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)

If f(x) = x2 + 3x + 5, evaluate f(x

+ 3).

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)

If 𝑓 𝑥 = 2𝑥 − 1 and 𝑔 𝑥 = 𝑥2 + 𝑥 − 2

1) Find 𝑓 + 𝑔 𝑥 and 𝑓 + 𝑔 3 .

If 𝑓 𝑥 = 2𝑥 − 1 and 𝑔 𝑥 = 𝑥2 + 𝑥 − 2

2) Find 𝑓 − 𝑔 𝑥 and 𝑓 − 𝑔 4 .

If 𝑓 𝑥 = 2𝑥 − 1 and 𝑔 𝑥 = 𝑥2 + 𝑥 − 2

3) Find 𝑓 ∙ 𝑔 𝑥 and 𝑓 ∙ 𝑔 2 .

If 𝑓 𝑥 = 2𝑥 − 1 and 𝑔 𝑥 = 𝑥2 + 𝑥 − 2

4) Find 𝑓

𝑔(𝑥) and

𝑓

𝑔(3).

Interval NotationInequality Graph Interval Notation

x < 2

𝑥 ≥ 2

2 < x < 5

−3 ≤ 𝑥 ≤ 0

ℝ

𝑥 ≠ 1

𝑥 ≠ −2, 𝑥 ≠ 3

𝑥 < 2 𝑜𝑟𝑥 ≥ 5 𝑎𝑛𝑑 𝑥 ≠ 8