Functions & Sequences

Question 1

“Sum of first n even whole numbers”

Answer 1

=

n(n+1)

Question 2

“Sum of first n odd whole #’s”

Answer 2

=

n²

Question 3

Compound Functions

f(f(x))

f(g(x))

f(g(h(x)))

Answer 3

The output of the initial function is the input of the next function

Question 4

Domain of Function

Answer 4

The set of all inputs a function can use

Keep in mind…

(1) you can’t take the square root of a neg. #

(2) you can’t divide by 0

Question 5

Determining the Range of a Function

Answer 5

(1) Must be in this form:

kxⁿ + c

(2) n = positive integer
(3) k is not = 0

* xⁿ= 0

If all three above checkout then…

if k > 0 then the range of f(x) = all real #’s _> _c

**if **k < 0 then the range of f(x) = all real #’s < c

Question 6

Arithmetic Sequence Equation

Answer 6

a_n= a₁ + (n-1)d

a_n = n^th term of the sequence

a₁ = 1^st term of the sequence

d = common difference

Question 7

Σ of the 1^st “n” terms in a sequence

Answer 7

=

n₁ = 1^st term in sequence

a_n = n^th term

Question 8

Geometric Sequence Formula

Answer 8

a_n = n^th term

a₁ = 1^st term

r = common ratio