Everything Maths Grade 10

51.Givenh(x) =x^2 4 andk(x) =x^2 + 4. Answer the questions that follow.

a)Sketch both graphs on the same set of axes.

b)Describe the relationship betweenhandk.

c)Give the equation ofk(x)reflected about the liney= 4.

d)Give the domain and range ofh.

52.Sketch the graphs off() = 2sinandg() =cos 1 on the same set of axes. Use your sketch to
determine:
a)f(180°) b)g(180°) c)g(270°)f(270°)
d)The domain and range ofg. e)The amplitude and period off.

53.The graphs ofy=xandy=

8

x

are shown in the following diagram.

0

A

B

C

D

y=x

G

E

F

x

y

Calculate:

a)The coordinates of pointsAandB.

b)The length ofCD.

c)The length ofAB.

d)The length ofEF, givenG(2; 0).

54.Given the diagram withy= 3 x^2 + 3andy=

18

x

.

0

A B

C

D

y=^18 x

y= 3 x^2 +3

x

y

Chapter 6. Functions 231