Lesson 2: Introduction to Power Functions
1. An __________ is a series of terms each separated by the operations of addition or subtraction.
2. An __________ balances or relates two expressions of equal value.
3. A ___________ relates two variables: one independent and one dependent.
4. A has the form a
n x n + a
n -1 x n -1
●
+ a
n -2 x n - 2 + . . . . a
3 x 3 + a
2 x 2 + a x + a
0 where n is a whole number and the __________ of the function (fxn) is n.
●
●
● x is a variable. a is the numerical coefficient of a term; a
n of the highest degree term.
is the (LC) a
0 is the term without a variable, the constant term.
5. A polynomial function has the form f(x) = a
n x n
●
+ a
n -1 x n -1 + a
n -2 a whole number x n - 2 + . . . . a
3 x 3 + a
2 x 2 + a x + a
0 where a function is a polynomial in the form y = a
n
x n , where n is
● power fxns have similar characteristics depending on whether they are even
●
● degree fnxs or odd degree fxns even degree power fnxs have a line of symmetry in the y-axis, the line x = 0 odd degree power fxns have point symmetry about the origin, (0, 0)
6. Symmetry
A graph has line symmetry if there is a line ________ that divides the graph into two parts such that each part is a reflection of the other in the line x = a.
A graph has point symmetry about a point
(a, b) if each part of the graph on one side of the point (a, b) can be rotated ____ to coincide with part of the graph on the other side of (a, b).
7. Special Names for Functions:
Power Function y=a y=ax y=ax 2 y=ax 3 y=ax 4 y=ax 5
Degree Name

8. Interval Notation
● There are several ways to describe the domain of a fxn. One method we already know using number lines. For example:
{x ε R -2 ≤ x < 1} {x ε R x ≤ 3} {x ε R x > -2}
Bracket Method : This is a way of short-forming.
● Square brackets [ ] mean that we include endpoints and round brackets ( ) mean that we exclude endpoints.
● Intervals that are infinite are expressed using the symbol ∞ (positive infinity) and -∞
(negative infinity). The set can approach but not include infinity.
● For example:
-3 ≤ x < 2
[-3,2) x ≤ 3
(-∞, 3] x > 2
(2, ∞) x
(-∞, ∞)
9. End Behaviour
● End behaviour refers to where the fxn is coming from and where it is going.
● This is most easily described using quadrants and is characteristic for even degree and odd degree fxns.
● For our examples we will use the most basic odd degree fxn ( y = x) and the most basic even degree fxn ( y = x 2 ).
● Read fxns from LEFT to RIGHT!
Fxn Type
Sign of Leading
Coefficient
End Behaviour
Even Degree
Even Degree
Odd Degree
Odd Degree
+
-
+
y = x y = - x y = x
2 y = - x
2