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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?
Input (x)
DOMAIN
Output (y)
RANGE
A function is a rule that establishes a
relationship with an input and an
output.
What is a Function?
Input (x)
DOMAIN
Output (y)
RANGE
function – a relation where each
input matches up with exactly one
output
f
x
y
(inputs)
(outputs)
1
-1
2
0
3
1
5
3
8
6
relation – a pairing of input
(domain) and output (range)
numbers
domain
f
x
y
(inputs)
(outputs)
1
-1
2
0
3
1
5
3
8
6
relation – a pairing of input
(domain) and output (range)
numbers
* A set of ordered pairs
f
domain range
x
y
(inputs)
(outputs)
1
-1
2
0
3
1
5
3
8
6
relation – a pairing of input
(domain) and output (range)
numbers
Domain = D {1, 2, 3, 5, 8}
Range = R {-1, 0, 1, 3, 6}
independent dependent
x
f (x)
-1
3
0
3
1
3
3
3
6
3
6
3
3
3
Is f (x) a function?
YES!
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.
x
f (x)
Is f (x) a function?
NO!
1
3
0
13
WHY? Check yourself!
1
-3
4
3
• Does each input match up
with exactly one output?
6
5
6
5
3
1
• If an input value is put in
multiple times, do you get
the same output every
time?
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! 
Relation: Different Form
{(1,-1),(2,0),(3,1),(5,6),(2,4)}
Is this relation a function?
f
x
y
(inputs)
(outputs)
-6
-9
Find:
-5
-7
1. domain
-1
3
2. range
2
4
6
7
3
-7
3. y if x = -1
4. x if y = 7
f
x
y
(inputs)
(outputs)
-6
-9
-5
-7
-1
3
2
4
6
7
function notation
For function f:
y=3
f (-1) = 3
“The value at x = -1 is 3.”
Graph it!
x
f (x)
1
3
0
13
1
-3
4
3
6
5
6
5
3
1
Is f (x) a function?
NO!
Vertical Line Test – as a vertical
line passes it never touches
more than one point on the
graph
Graph it!
g(x) = -3x – 6
Is g(x) a function?
YES!
f (x) = mx + b
linear function
Is this a graph of a function?
NOT A
FUNCTION!
Is this a graph of a function?
FUNCTION!
Evaluating Functions
Remember 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).
EVALUATING CHALLENGE!!!
D. If f(x) = 4x+9
Find
 f(2)
 f(-3)+7
 f(2y)
APPLICATION 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).
Algebra A/B
Homework:
1.7 Practice Worksheet (ODDS)