Everything Maths Grade 10

Step 2: Calculate the intercepts

For they-intercept, letx= 0:

g(x) =

2

x

+ 2

g(0) =

2

0

+ 2

This is undefined, therefore there is noy-intercept.

For thex-intercept, lety= 0:

g(x) =

2

x

+ 2

0 =

2

x

+ 2

2

x

= 2

)x= 1

This gives the point(1; 0).

Step 3: Determine the asymptotes

The horizontal asymptote is the liney= 2. The vertical asymptote is the linex= 0.

Step 4: Sketch the graph

 4  3  2  1 1 2 3 4

 3

 2

 1

1

2

3

4

5

6

0

g(x) =x^2 + 2

(1; 0)

x

g(x)

Domain:fx:x 2 R; x̸= 0g

Range:fy:y 2 R; y̸= 2g

Worked example 11: Sketching a hyperbola

QUESTION

Sketch the graph ofy=

4

x

+ 7.

Chapter 6. Functions 173