Ch.1 Functions

Question 1

Definition of a function

Answer 1

A correspondence between 2 sets D (the domain) and C (the codomain), that assigns each element of D one and only one element of C
f : D –> C

Question 2

Range of f

Answer 2

The set of all images

Ran f = {f(x) : x ϵ Domf}

Question 3

What is the vertical line test?

Answer 3

If any vertical line intersects the curve more than once then the curve is not a function, otherwise it is

Question 4

A function is even if…

Answer 4

f(x) = f(-x) for all x in Dom f

Question 5

A function is odd if…

Answer 5

f(-x) = -f(x) for all x in Dom f

Question 6

Even and odd parts of a function

Answer 6

feven(x) = (1/2)f(x) + (1/2)f(-x)
fodd(x) = (1/2)f(x) - (1/2)f(-x)

Question 7

A function is surjective if…

Answer 7

Ran f = C

ie for every y in C there exists an x in D such that f(x) = y

Question 8

A function is injective if…

Answer 8

for all x1, x2 in D, with x1 ≠ x2, then f(x1) ≠ f(x2)

Question 9

What is the horizontal line test?

Answer 9

If no horizontal line intersects the graph of f more than once then f is not injective, otherwise it is

Question 10

What is a rational function?

Answer 10

A ratio of 2 polynomials f(x) = p(x) / q(x)