© John Wiley & Sons Australia, Ltd 2009 1

WorkSHEET 2.1 Relations and functions Name: ________________________ 1 State whether the following graphs are discrete

or continuous: Note: 𝐽 means “integers” 𝑅 means “Real numbers” (any number you can think of) (a) where x Î J

(b) where x Î R (c) where x Î {2, 3, 4, 5, 6}

(d) where -2 < x < 2

(a) where x Î J

Discrete (as J is integer values only) (b) where x Î R

Continuous (c) where x Î {2, 3, 4, 5, 6}

Discrete

(d) where -2 < x < 2

Not continuous as is undefined.

4

2 What is the domain and range of each of the graphs:

a)

b)

c) where x Î {2, 3, 4, 5, 6}

d) where -2 < x < 2

(a) where x Î J Domain: −∞ < 𝑥 < ∞

Range: −∞ < 𝑦 < ∞

(b) where x Î R Domain: −∞ < 𝑥 < ∞

Range: −2 < 𝑦 < ∞

(c) where x Î {2,3,4,5,6} Domain: x Î{2, 3, 4, 5, 6} Range: y Î{0, 1, , , 2}

(d) where -2 < x < 2

Domain: −2 < 𝑥 < 2 but 𝑥 ≠ 0 Range: − +

,< 𝑦 < +

, but 𝑦 ≠ 0

4

,24 += xy

,22 -= xy

,2-= xy

,12xy =

,24 += xy

,22 -= xy

,2-= xy

,12xy =

01

=y

,24 += xy

,22 -= xy

,2-= xy

y = 1x,

,24 += xy

,22 -= xy

,2-= xy

2 3

y = 1x,

Maths Quest Maths B Year 11 for Queensland Chapter 2: Relations and functions WorkSHEET 2.1

© John Wiley & Sons Australia, Ltd 2009 2

3 What is the domain and range of each of the following, in interval notation? (a) (b) (c)

(d)

(a)

Domain: −∞ < 𝑥 < ∞ Range: −∞ < 𝑦 < ∞

(b)

Domain: −∞ < 𝑥 < ∞ Range: 0 ≤ 𝑦 < ∞

(c)

Domain: −∞ < 𝑥 < 3 Range: 0 ≤ 𝑥 < ∞

(d)

Domain: −∞ < 𝑥 < ∞ but 𝑥 ≠ 2 Range: −∞ < 𝑦 < ∞ but 𝑦 ≠ 0

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4 Consider the following sets of coordinates and determine the type of relation for each. (a) {(-3, 2), (4, -2), (-3, -2), (4, 2)} (b) {(1, 1), (1, 3), (1, 5)} (c) {(2, -3), (3, -3), (4, -3)} (d) {(1, 1), (2, 2), (3, 3)}

(a) Many-to-many relation (as x-values

double up and y-values double up) (b) One-to-many relation (as one x-value

corresponds to many y-values) (c) Many-to-one relation (as many x-values

correspond to one y value) (d) One-to-one relation (a different x-value

corresponds to each y-value)

4

5 Which of the following relations are functions? (a) {(1, 3), (2, 2), (3, 1), (4, 1), (5, 7), (7, 5), (6, 5)} (b) x2 + y2 = 25 (c) y > 2x + 1 (d)

(a) Function (b) Not a function. (-5, 0), (5, 0) (c) Not a function. (1, 4), (1, 5) (d) Function

4

xy 23-=

442 +-= xxy

y = 6− 2x

21-

=x

y

xy 23-=

442 +-= xxy

y = 6− 2x

21-

=x

y

4+= xy