1.7 functions ccss content standards f.if.1 understand that a function from one set (called the...
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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!
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!
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
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!!!
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