Math - 2017-18
A.7 and *A.7 - Relations
A.7 The student will investigate and analyze function (linear and quadratic) families and their characteristics both algebraically and graphically, including
a) determining whether a relation is a function;
b) domain and range;
c) zeros of a function;
d) x- and y-intercepts;
e) finding the values of a function for elements in its domain; and
f) making connections between and among multiple representations of functions including concrete, verbal, numeric, graphic, and algebraic.
A.7 The student will investigate and analyze linear and quadratic function families and their characteristics both algebraically and graphically, including
a) determining whether a relation is a function;
b) domain and range;
c) zeros;
d) intercepts;
e) values of a function for elements in its domain;
f) connections between and among multiple representations of functions using verbal descriptions, tables, equations, and graphs.
Bloom's Level: Analyze
BIG IDEAS
- I can compare the cost of
pizza with number of toppings, find the correlation between number of hours
spent in the sun and development of skin cancer, match the amount of money put
into a vending machine with the kind of selection that comes out, and equate
the growth of plants with amount of food and water they receive.
- I
will be able to model various kinds
of mathematical relationships and express those relationships in different
ways.
UNDERSTANDING THE STANDARD
- A set of data may be characterized by patterns,
and those patterns can be represented in multiple ways.
- Graphs can be used as visual representations to
investigate relationships between quantitative data.
- Inductive reasoning may be used to make
conjectures about characteristics of function families.
- Each element in the domain of a relation is the
abscissa of a point of the graph of the relation.
- Each element in the range of a relation is the
ordinate of a point of the graph of the relation.
- A relation is a function if and only if each
element in the domain is paired with a unique element of the range.
- The values of f(x) are the ordinates of
the points of the graph of f.
- The object f(x) is the unique object in the range of
the function f that is associated
with the object x in the domain of f.
- For each x
in the domain of f, x is a member of the input of the
function f, f(x) is a member of the
output of f, and the ordered pair [x, f(x)] is a member of f.
- An object x
in the domain of f is an x-intercept or a zero of a function f if and only if f(x) = 0.
- Set builder notation may be used to represent
domain and range of a relation.
2016 VDOE Curriculum Framework - AI.7 Understanding
· A relation is a function if and only if each element in the domain is paired with a unique element of the range.
· Functions describe the relationship between two variables where each input is paired to a unique output.
· Function families consist of a parent function and all transformations of the parent function.
· The domain of a function is the set of all possible values of the independent variable.
· The range of a function is the set of all possible values of the dependent variable.
·
For each x in the domain of f, x is a member of the
input of the function f, f(x) is a member of the output of f, and the ordered pair
(x, f(x)) is a member of f.
· A value x in the domain of f is an x-intercept or a zero of a function f if and only if f(x) = 0.
· Given a polynomial function f(x)the following statements are equivalent for any real number, k, such that f(k) = 0:
k is a zero of the polynomial function f(x), located at (k, 0);
(x – k)is a factor of f(x);
k is a solution or root of the polynomial equation f(x) =0; and
the point (k, 0) is an x-intercept for the graph of y = f(x).
· The x-intercept is the point at which the graph of a relation or function intersects with the x-axis. It can be expressed as a value or a coordinate.
· The y-intercept is the point at which the graph of a relation or function intersects with the y-axis. It can be expressed as a value or a coordinate.
· The domain of a function may be restricted by the practical situation modeled by a function.
· Solutions and intervals may be expressed in different formats, including set notation or using equations and inequalities.
- Examples may include:
Equation/ Inequality |
Set Notation |
x = 3 |
{3} |
x = 3 or x = 5 |
{3, 5} |
y≥ 3 |
{y: y ≥ 3} |
Empty (null) set ∅ |
{ } |
ESSENTIALS
The student will use problem solving, mathematical communication, mathematical reasoning, connections, and representations to
A.7a_{1} Determine whether a relation, represented by a set of ordered pairs, a table, or a graph is a function.
· A.7a_{1 }Determine whether a relation, represented by a set of ordered pairs, a table, a mapping, or a graph is a function.
A.7f_{1} Represent relations and functions using concrete, verbal, numeric, graphic and algebraic forms. Given one representation, students will be able to represent the relation in another form.
· A.7f_{1 }Represent relations and functions using verbal descriptions, tables, equations, and graph. Given one representation, represent the relation in another form.
A.7bcd_{1} Identify the domain, range, zeros and intercepts of a function presented algebraically or graphically.
· A.7bcd_{1 }Identify the domain, range, zeros, and intercepts of a function presented algebraically or graphically.
A.7c_{1} For each x in the domain of f, find f(x).
· A.7e_{1 }For any value, x, in the domain of f, determine f(x).
A.7f_{2} Detect patterns in data and represent arithmetic and geometric patterns algebraically.
· A.7abcdef_{1 }Investigate and analyze characteristics and multiple representations of functions with a graphing utility.
KEY VOCABULARY
function, relation, ordered pairs, table, graph,
domain, range, zeros, intercepts, patterns, arithmetic, geometric, quantitative
data, inductive reasoning, conjectures, abscissa, ordinate, element, f(x), input, output, member, set builder notation