Polynomial Functions

Question 1

Function VS Relation

(Every ___ is a ___ but not every ___ is a ___)

Answer 1

Function: (vertical line test)
- Relation with each independent variable has only 1 dependent variable

Relation:
- Values of independent variables are paired with values of the dependent variable

Every function is a relation but not every relation is a function

Question 2

Zero exponent

Answer 2

A^0 = 1

-A^0 = -1

Question 3

Product law

Answer 3

A^x • A^y = A^x+y

Question 4

Quotient law

Answer 4

A^x/A^y = A^x-y

Question 5

Negative exponent

Answer 5

A^-x = 1/A^x

(A/B)^-x = (B/A)^x

Question 6

Power of a quotient

Answer 6

(A/B)^n = (A^n/B^n)

Question 7

Power of a power

Answer 7

(A^x)^y = A^xy

Question 8

Power of a product

Answer 8

(AB)^n = A^n B^n

Question 9

Linear Functions

Answer 9

• Degree of 1
• Graph = Linear
• First diff = Constant

Question 10

Linear function forms

Answer 10

Standard: Ax + By + c = 0

Slope (y-intercept): y = mx + b

Slope form y2 - y1/x2 - x1

Question 11

F(0) = ?

3F(x) = ?

Answer 11

F(0) = x = 0

3F(x) = 3[…]

Question 12

GCF

Answer 12

Greatest Common Factor

Question 13

ST

Answer 13

Simple Trinomial

PSN (Play Station Network) (Product Sum Number)

Question 14

DOS

Answer 14

Difference Of Square

Question 15

CT

Answer 15

Complex Trinomial

Question 16

Vertex form

Answer 16

Y = a(x - h)^2 + k

Question 17

Factored form

Answer 17

Y = a(x - r)(x - s)

X intercept form

Question 18

Factored form

Answer 18

Y = a(x - r)(x - s)

X intercept form

Question 19

Standard to Vertex

Answer 19

Complete the Square

Question 20

Mapping notation

Answer 20

(x,y) -> (x/k + d, ay + c)

Question 21

Quadratic functions

Answer 21

• degree of 2
• graph is parabola
• second diff same

Question 22

What are the transformations:

Y = af(k(x - d)) + c

Answer 22

A:
- vertical stretch/compress (0<a<1)
- (-a) = reflection on x axis (vertical)

K:
- horizontal stretch/compress
- (-k) = reflect on y axis (horizontal)

D:
- horizontal translate

C:
- vertical translate

Question 23

Interval notation

Answer 23

(-2,6]

Question 24

Set builder notation

Answer 24

{xeR , -2 < x =< 6}

Question 25

What makes a “Polynomial function”/rules of polynomial function

Answer 25

- atleast 1 x - no negative exponents - no fraction exponents - no variable exponents - no sin/cos

Question 26

Degree

Answer 26

Greatest power of x

Question 27

Leading coefficient

Answer 27

Coefficient of greatest power of x

Question 28

Smallest degree

Answer 28

Number of turning points + 1

Question 29

End behaviour (Positive odd)

Answer 29

Q3 -> Q1

Question 30

End behaviour (Negative odd)

Answer 30

Q2 -> Q4

Question 31

End behaviour (Positive even)

Answer 31

Q2 -> Q1

Question 32

End behaviour (Negative even)

Answer 32

Q3 -> Q4

Question 33

“U”

Answer 33

Unison

Question 34

Local minimum

Answer 34

Least y value on interval

Question 35

Local maximum

Answer 35

Greatest y value on interval

Question 36

Global minima/maxima

Answer 36

Absolute max/min points

Question 37

Power function

Answer 37

Simplest type of polynomial function

Question 38

Polynomial function

Answer 38

Name based on degree (ex: cubic) Y = ax^n - a is constant - x is variable

Question 39

Odd degree x intercepts ???

Answer 39

- atleast 1 - max n - inflection through x-axis

Question 40

Even degree x intercepts ???

Answer 40

- 0 to N - bounce

Question 41

Odd degree number of global max/min ????

Answer 41

Doesn’t exist

Question 42

Even degree number of global max/min ????

Answer 42

Max = a<0 Min = a>0

Question 43

Is an even degree function always an even function?

Answer 43

No (SAME WITH ODD)

Question 44

Even functions info

Answer 44

- symmetry on y-axis - f(-x) = f(x) If you sub in (-x) into (x) then it’ll end the same as start

Question 45

How to identify Odd functions

Answer 45

- rotationally symmetrical - rotate 180 (vert + hori reflect) - if you sub in (-x) for (x) the signs of each terms will switch

Question 46

Transformations

Answer 46

Y = af (k (x-d)) + c

Question 47

Y = af (k (x-d)) + c A TRANSFORMATIONS

Answer 47

A < 0 = reflect in x-axis A > 1 = vertical stretch by a factor of A 0 < A < 1 = vertical compress by a factor of A

Question 48

Y = af (k (x-d)) + c K TRANSFORMATIONS

Answer 48

- K > 1 = horizontal compress by a factor of 1/k - 0 < k < 1 = horizontal stretch by a factor of 1/k - k < 0 = reflect in y axis, horizontal reflection

Question 49

Y = af (k (x-d)) + c C TRANSFORMATIONS

Answer 49

- c > 0 = vertical translate up - c < 0 = vertical translate down

Question 50

Y = af (k (x-d)) + c D TRANSFORMATIONS

Answer 50

- d > 0 = horizontal translate right - d < 0 = horizontal translate left

Question 51

Intervals of increase

Answer 51

Intervals where y increases as x increases (Thing goes up even if below x axis)

Question 52

Intervals of decrease

Answer 52

Intervals where y decreases as x increases (Thing goes down even if above x axis)

Question 53

Positive intervals

Answer 53

Interval where the function lies above x axis

Question 54

Negative intervals

Answer 54

Intervals where the function lies below the x axis

Question 55

Polynomial function of degree n, where n is a positive integer, the n-th differences:

Answer 55

- are equal (constant) - have the same sign as leading coefficient

Question 56

How do you find out he degree of the polynomial function

Answer 56

Number of finite differences

Question 57

How do you find the sign of the leading coefficient?

Answer 57

The sign of the final finite differences

Question 58

How do you find the value of the leading coefficient?

Answer 58

A3! = -6 The value of the leading coefficient is a

Question 59

Order

Answer 59

If a polynomial function has a factor (x-a) that is repeated n times, then x = a is a zero of order n INDIVIDUAL Exponent of the thing

Question 60

Expand: (a+b)^2

Answer 60

(a^2 +2ab + b^2) (a-b)^2: (a^2 +2ab - b^2)

Question 61

Expand a^2 - b^2

Answer 61

(a + b)(a - b)