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Polynomial
Functions
YOUR NAME:

Day 1 - Objective
Today
I can identify and define a
function and a polynomial
function.
STANDARD
APR.A.1
Understand that polynomials form a system analogous to the integers, namely, they are closed under
the operations of addition, subtraction, and multiplication; add, subtract, and multiply polynomials.
Beyond quadratic

Precalculus ( Polynomial Functions.pptx)

Vocabulary
• A set of ordered pairs is also called a relation.
• The domain is the set of x-coordinates (first
components) of the ordered pairs.
• The range is the set of y-coordinates (second
components) of the ordered pairs.

Determine the domain and range of the relation
{(4,9), (–4,9), (2,3), (10, –5)}
• Domain is the set of all the first coordinates of the
ordered pairs: {4, –4, 2, 10}
• Range is the set of all the second coordinates of
the ordered pairs: {9, 3, –5}
Example

Input (Animal)
●Polar Bear
●Cow
●Chimpanzee
●Giraffe
●Gorilla
●Kangaroo
●Red Fox
Output (Life Span)
20
15
10
Find the domain and range of the following
relation.
Example

Domain is {Polar Bear, Cow, Chimpanzee,
Giraffe, Gorilla, Kangaroo, Red Fox}
Range is {20, 15, 10, 7}
Example (cont)

Some relations are also functions.
A function is a relation in which each first
component in the ordered pairs corresponds to
exactly one second component.
THINK OF A FUNCTION AS A MACHINE- SOMETHING GOING IN
AND SOMETHING COMING OUT!
Functions

Is the relation{(4,9), (–4,9), (2,3), (10, –5)}, also a
function?
Since each element of the domain is paired with
only one element of the range, it is a function.
Note: It’s okay for a y-value to be assigned to
more than one x-value, but an x-value cannot be
assigned to more than one y-value (has to be
assigned to ONLY one y-value).
Example

Is the relation y = x2
– 2x a function?
Since each element of the domain (the
x-values) would produce only one element
of the range (the y-values), it is a function.
Example

Is the relation x2
– y2
= 9 a function?
Since each element of the domain (the
x-values) would correspond with 2
different values of the range (both a
positive and negative y-value), the
relation is NOT a function.
Example

Graphs can be used to determine if a
relation is a function.
Vertical Line Test
If a vertical line can be drawn so that it
intersects a graph more than once, the
graph is not the graph of a function.
Vertical Line Test

Use the vertical line
test to determine
whether the graph to
the right is the graph
of a function.
x
y
Since no vertical line
will intersect this
graph more than
once, it is the graph
of a function.
Example

Use the vertical line
test to determine
whether the graph to
the right is the graph
of a function.
Since vertical lines can
be drawn that intersect
the graph in two points,
it is NOT the graph of a
function.
x
y
Example

Since the graph of a linear equation is a line, all
linear equations are functions, except those
whose graph is a vertical line
Note: An equation of the form y = c is a horizontal
line and IS a function.
An equation of the form x = c is a vertical line and
IS NOT a function.
Vertical Line Test

Find the domain and
range of the function
graphed to the right.
Use interval
notation. x
y
Domain is [–3, 4]
Domain
Range is [–4, 2]
Range
Example

Find the domain
and range of the
function graphed to
the right. Use
interval notation. x
y
Domain is (– ∞, ∞)
Domain
Range is [– 2, ∞)
Rang
e
Example

Helpful Hint
Note that f(x) is a special symbol in mathematics
used to denote a function. The symbol f(x) is read
“f of x.” It does not mean f • x (f times x).

Find each function value.
a. If f(x) = 4x – 1, find f(2).
f(2) = 4(2) – 1 = 7
b. If g(x) = x2
– 2x, find g(–3).
g(–3) = (–3)2
– 2(–3) = 9 – (–6) = 15
Example

To Learn
What is a polynomial function?
A polynomial function is a function that involves
only non-negative integer powers or only positive
integer exponents of a variable in an equation like
the quadratic equation, cubic equation, etc

Polynomial Functions
The largest exponent within the polynomial
determines the degree of the polynomial.
Quartic
4
Cubic
3
Quadratic
2
Linear
1
Name of
Function
Degree
Polynomial Function
in General Form

Polynomial in Standard Form:
1. The coefficient of the first term is
the LEADING COEFFICEINT
2. The exponent of the first term is
the DEGREE of the Polynomial
3. A term that has no variable is a
CONSTANT TERM.

Work in pairs to and complete the following problems.

Day 2 - Objective
Today
I can add and subtract
polynomials.
STANDARD
APR.A.1
Beyond quadratic

Practice
.
Add or Subtract the following:

Practice
.
Add or Subtract the following:
=
=

evaluate
Stations:
1.Khan Academyassigned on google classroom
2. Worksheet

Day 3 - Objective
Today
I can multiply functions
including multiplying a
binomial by a trinomial.
STANDARD
APR.A.1
Beyond quadratic

evaluate
Stations:
1.Khan Academy
2. Worksheet
On Google Classroom

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Precalculus ( Polynomial Functions.pptx)

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