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Intro to Function Relationships – 7 days
Lesson Topics
Objective
Example Problems
Common Core
Standards
2008 State
Standards
Is the
relationship a
function?
Determine if a
relationship is a function
from a table, list of points
and a graph.
Ex. 1:
Determine if each is a function
and explain how you know.
HS.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).
MA09-S03-C03-01
Create and explain the
need for equivalent forms of
an equation or expression
Identify the domain and
range from a table of
values, list of points and
a graph. Explain why the
data set is a function or
not and how the sets are
related.
Ex. 1:
If the function h(n) gives the
number of person-hours it
takes to assemble n engines in
a factory, then whole numbers
would be an appropriate
domain for the function.
HS.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
MA09-S03-C02-07
Determine domain and
range of a function from an
equation, graph, table,
description, or set of
ordered pairs.
Domain and
Range of
Functions
Ex. 2:
MA09-S03-C02-02
Determine if a relationship
represented by an equation,
graph, table, description, or
set of ordered pairs is a
function.
identify the domain and range
for the function.
Input
2 4 6 8 10
Output
- - - - 3 5 7 9 11
Ex. 3:
Determine the range of the
function f(x) = -3x – 4 given
the domain set {-1, 0, 1, 2}.
Evaluating
Functions
Evaluate (substitute)
functions given a
specified domain (x)
value.
Basic Ex.1:
If f ( x )  x 2  4x  12 , find f (2).
Core Ex.2:
Let f ( x )  2( x  3)2 . Find f (3) ,
1
f ( ) , f (a ) , and f (a  h)
2
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).
HS.F-IF.5.
Relate the domain of a
function to its graph and,
where applicable, to the
quantitative relationship it
describes. For example, if
the function h(n) gives the
number of person-hours it
takes to assemble n
engines in a factory, then
the positive integers
would be an appropriate
domain for the function.
HS.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.
MA09-S03-C02-03
Use function notation;
evaluate a function at a
specified value in its
domain.
Applications with
function notation
Analyze a real-world
situation to write a
function, explain what
each value of the function
means, relate the domain
to the range and evaluate
given a specified domain.
Ex.1:
If P(t) is the population of Tucson t
years after 2000, interpret the
statements P(0) = 487,000 and
P(10)-P(9) = 5,900.
HS.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.
MA09-S03-C02-03
Use function notation;
evaluate a function at a
specified value in its
domain.
HS.F-IF.5.
Relate the domain of a
function to its graph and,
where applicable, to the
quantitative relationship it
describes. For example, if
the function h(n) gives the
number of person-hours it
takes to assemble n
engines in a factory, then
the positive integers
would be an appropriate
domain for the function.
These standards should be evident throughout the unit (may not be in each lesson).

HS.A-SSE.1: Interpret expressions that represent a quality in terms of its context.
a. Interpret parts of an expression, such as terms, factors and coefficients.

HS.F-IF.9: Compare properties of two functions each represent in a different way (algebraically, graphically, numerically
in tables, or by verbal descriptions).