Everything Maths Grade 10

SOLUTION

Step 1: Examine the standard form of the equation

We see thata < 0 therefore the graph lies in the second and fourth quadrants.

Step 2: Calculate the intercepts

For they-intercept, letx= 0:

y=

4

x

+ 7

=

4

0

+ 7

This is undefined, therefore there is noy-intercept.

For thex-intercept, lety= 0:

y=

4

x

+ 7

0 =

4

x

+ 7

4

x

= 7

)x=

4

7

This gives the point

(

4

7

; 0

)

.

Step 3: Determine the asymptotes

The horizontal asymptote is the liney= 7. The vertical asymptote is the linex= 0.

Step 4: Sketch the graph

 6  5  4  3  2  1 1 2 3 4 5 6

 2

2

4

6

8

10

12

14

0

y=

 4

x

+ 7

y= 7

(^47 ; 0)

x

y

Domain:fx:x 2 R; x̸= 0g

Range:fy:y 2 R; y̸= 7g

Axis of symmetry:y=x+ 7andy=x+ 7

174 6.4. Hyperbolic functions