Functions and Function Notation Notes

Identifying Functions

Precalculus

Open Ended

What do we remember of finding if tables, graphs and charts are functions?

FUNCTION

a specific kind of relationship where every input has exactly one output.
(x-values are used ONLY one time. y-values can be used more than once.)

​Testing for Functions

​There are different tests for different ways of communicating functions:

​1. In a sentence, or a table, consider whether any given x value gives multiple y values at a time.

​

​2. In a graph, use the vertical line test. If you can draw a vertical line through two points on the relation, then it is not a function.

​

​3. Solve the equation for y. If there are two possible solutions of y for one given x, then it is not a function.

Multiple Choice

Function or not a function

• function

• not a function

Multiple Choice

Which set of ordered pairs is a function?

• {(9,5), (10,5), (9,-5), (10,-5)}

• {(3,4), (4,-3), (7,4), (3, 8)}

• {(6,-5), (7, -3), (8, -1), (9, 1)}

• {(2, -2), (5, 9), (5, -7), (1, 4)}

Multiple Choice

Function or not a function

• function

• not a function

Fill in the Blanks

The graph of a function must pass the

line test.

Multiple Choice

Function or not a function

• function

• not a function

Multiple Choice

Is this a function

• Function
• Not a Function

Multiple Choice

Which of the following is NOT a function?

Multiple Choice

Is this a function?

• Function
• Not a Function

Poll

How comfortable are you with understanding how to find a function within the various mediums we saw today (Graphing, Tables, Mapping, Ordered Pairs)?

• Very Much Ready

• Ready but nervous

• Somewhat But I Still need guidance

• Can we redo, Teacher?

Function Notation

Objective: Evaluate functions written in function notation.

Youtube video link

https://www.youtube.com/watch?v=Kj3Aqov52TY

Function Notation

a specific way to write a relation when it is a function. ​

General Function Notation: f(x)

Said out loud: "f of x"

Example:

y = 4x - 1 is a function. f(x) = 4x - 1

Read as 'f of x' = 4x - 1

How to Evaluate

• Given the function h

• Substitute 3, a domain value, on both sides of = for k

• Use order of operations (PEMDAS) to simplify

Multiple Choice

If f(x) = 2x + 1, find f(1).

• f(1) = 1

• f(1) = 4

• f(1) = 0

• f(1) = 3

Multiple Choice

Evaluate f(-2) if f(x) = x + 3

• -1
• 1
• 5
• -5

Multiple Choice

For the function f(x) = -3(x-1) find f(0).

• 0
• -3
• 3
• -1

Multiple Choice

If I know that f(2) = 4, what is another way I can write my answer?

• 2,4

• (2, 4)

• That is the only way to write it.

Function Notation and Graphs

f(x) = y

Multiple Choice

Use the graph find x when f(x) = 1

• -3

• 3

• 3, -3

• 0

Multiple Choice

Use the graph find x when f(x) = 4

• 2

• 4

• 3

• 0

Multiple Choice

Use the graph to evaluate f(2)=

• 2

• -2

• 3

• 0

Open Ended

If you are having difficulty with the lesson, what part of the lesson would you like for me to revise or adjust to better help you understand?