1.7 FUNCTIONS

CCSS

Content Standards

F.IF.1 Understand that a function from one set (called the domain) to another set (called the range) assigns to each element of the domain exactly one element of the range. If f is a function and x is an element of its domain, then f(x) denotes the output of f corresponding to the input x. The graph of f is the graph of the equation y = f(x).

F.IF.2 Use function notation, evaluate functions for inputs in their domains, and interpret statements that use function notation in terms of a context.

Mathematical Practices

3 Construct viable arguments and critique the reasoning of others.

Common Core State Standards © Copyright 2010. National Governors Association Center for Best Practices and Council of Chief State School Officers. All rights reserved.

You solved equation with elements from a replacement set.

• Determine whether a relation is a function.

• Evaluate functions.

What is a Function?

A function is a rule that establishes a relationship with an input and an output.

Input (x)

Output (y)

DOMAIN

RANGE

What is a Function?

function – a relation where each input matches up with exactly one output

Input (x)

Output (y)

DOMAIN

RANGE

x(inputs)

y(output

s)

1 -1

2 0

3 1

5 3

8 6

f

relation – a pairing of input (domain) and output (range) numbers

x(inputs)

y(output

s)

1 -1

2 0

3 1

5 3

8 6

f

relation – a pairing of input (domain) and output (range) numbers

* A set of ordered pairs

domain

x(inputs)

y(output

s)

1 -1

2 0

3 1

5 3

8 6

f

relation – a pairing of input (domain) and output (range) numbers

domain range

Domain = D {1, 2, 3, 5, 8}

Range = R {-1, 0, 1, 3, 6}

independentdependent

x f (x)

-1 3

0 3

1 3

3 3

6 3

6 3

3 3

Is f (x) a function?

function – a relation where each input matches up with exactly one output

If an input value is put in multiple times, you will get the same output every time.

YES!

x f (x)

1 3

0 13

1 -3

4 3

6 5

6 5

3 1

Is f (x) a function?

WHY? Check yourself!

• Does each input match up with exactly one output?

• If an input value is put in multiple times, do you get the same output every time?

NO!

How can I tell if it’s a function?REAL WORLD EXAMPLES

How can I tell if it’s a function?REAL WORLD EXAMPLES People vs. Places

Relation: Different Form

{(1,-1),(2,0),(3,1),(5,6),(8,6)}

Is this relation a function?

Hint: Look at all of the input values first!

{(1,-1),(2,0),(3,1),(5,6),(8,6)}

Relation: Different Form

{(1,-1),(2,0),(3,1),(5,6),(2,4)}

Is this relation a function?

{(1,-1),(2,0),(3,1),(5,6),(2,4)}

x(inputs)

y(output

s)

-6 -9

-5 -7

-1 3

2 4

6 7

3 -7

Find:

1. domain

2. range

3. y if x = -1

4. x if y = 7

f

For function f:

y = 3f (-1) = 3

function notation

x(inputs)

y(output

s)

-6 -9

-5 -7

-1 3

2 4

6 7

f

“The value at x = -1 is 3.”

x f (x)

1 3

0 13

1 -3

4 3

6 5

6 5

3 1

Is f (x) a function?

Vertical Line Test – as a vertical line passes it never touches more than one point on the graph

NO!

Graph it!

Is g(x) a function?YES!

Graph it!g(x) = -3x – 6

f (x) = mx + b

linear function

Is this a graph of a function?

NOT AFUNCTION

!

Is this a graph of a function?

FUNCTION!

Evaluating FunctionsRemember f(x) is just function

notation!A. If f(x) = 3x – 4, find f (4).

f(4) =3(4) – 4 Replace x with 4.

=12 – 4 Multiply.

= 8 Subtract.

Answer: f(4) = 8

B. If f(x) = 3x – 4, find f(–5).

C. If h(t) = 1248 – 160t + 16t 2, find h(3).

D. If f(x) = 4x+9

Find f(2) f(-3)+7 f(2y)

EVALUATING CHALLENGE!!!

The function h(t) = 180 – 16t2 represents the height of a ball thrown from a cliff that is 180 feet above the ground.

Find h(2z).

APPLICATION CHALLENGE!!!

Homework:

1.7 Practice Worksheet (ODDS)

Algebra A/B