Let’s Review Functions

1. How do I name polynomials?

2. What is interval notation?

3. What is the domain & range of a function?

4. How do I find the intercepts of a functions graphically and algebraically?

Daily Questions…….

I. MONOMIALS:

A. A monomial is _______________

B. Some examples of monomials are:

a number, variable, or a product of numbers and variables.

x -20 4y -3a5

POLYNOMIALS:

A. A polynomial is the ________ or ___________ of monomials.

B. An example of a polynomial in one variable, x, would be

C. How many MONOMIALS are there in the above polynomial?

monomialthe sum

x3+6x2+12x+8

4

III.The _________exponent in the polynomial determines the DEGREE OF A POLYNOMIAL in one variable.

A. Example: The degree of –7x + 9 – 4x2 is ____ because ___ is the largest exponent in the polynomial.

B. Example: Find the degree of the following polynomial: x4 + 6x3 + 7x5 + 12x

largest

2 2

5

IV. STANDARD FORM

A. The terms of a polynomial are in STANDARD FORM if they are ordered from left to right in ______________ order; which means from the ____________ exponent to the smallest.

B. To write a polynomial in Standard Form, ______________ the terms of the polynomial in ______________ order according to the ________________ of the variables.

decreasing

largest

arrange

decreasing

exponent

IV. STANDARD FORM

C. Example: Write 9 + x – 4x3 in standard form.

D. Example: Write 3x2 – 2 + 4x – 5x3 in standard form.

– 4x3 + x + 9

– 5x3 + 3x2 + 4x - 2

V. Some polynomials have SPECIAL NAMES that are determined by the following:

A. Their _________ or

B. Their _________ of terms

C. Look at the chart for an explanation.

degree

number

Polynomial # of Terms

Name by # of Terms

DEGREE Name by Degree

12

8x

4x2 + 3

5x3 + x2

3x2 – 4x + 6

1 Monomial 0 Constant

1 Monomial 1 Linear

2 Binomial 2 Quadratic

2 Binomial 3 Cubic

3 Trinomial 2 Quadratic

How do we write in interval notation?

x < 2…. when you want include use a bracket [ when you want to exclude use a

parenthesis (

( , 2) Let’s draw a number line first….

Let’s do another type….4 9x Draw a number line first….

4,9

Domain and Range Remember that domain is all the x-

values (the input). Remember that range is all the y-

values (the output).

(2,4)

(-1,-5)

(4,0)

What is the domain of f(x)?

y = f(x)

Ex. 1

Domain

(2,4)

(-1,-5)

(4,0)

y = f(x)

What is the range of f(x)?

Range

Determine the domain and range….

With polynomials…. The DOMAIN is always All Reals,

The RANGE will be: All Reals, Lower Boundary to infinity, Negative infinity to Upper Boundary,

,

, LB,

,UB

Zeros/x-intercepts/Solutions/Roots

Where the graph

crosses the x-axis

What’s a zero?

x-interceptsWhere the graph

crosses the x-axis. Also called zeros.

1,0 & 5,0

Analyze the Graph of a Function

Zeros?

X= -3, -1, 2

y-intercepts

Where the graph crosses the y-axis

X and Y-intercepts Using Algebra

To find the x-intercepts, substitute y = 0 into the equation.

To find the y-intercepts, substitute x = 0 into the equation.

Ex. 1 y = 2x + 4Ex. 2 y = x2 - 9

y-intercepts

0,5

Analyze the Graph of a Function

Find the following

1.Domain:2.Range:3. Zeros:4. y-intercepts:

All realsAll reals-2, 1

(0, -4)

Find the following

1.Domain:2.Range:3. Zeros:4. y-intercepts:

All reals[-4, ∞)-2, 2

(0, -4)

-5 -4 -3 -2 -1 1 2 3 4 5

-5

-4

-3

-2

-1

1

2

3

4

5