Graph the function f(x) = 1=x (b) Hence, using appropriate translations and reflections, and stating them, graph f(x) = ??1 ?? 1 x + 2 Make sure that you show and label the intermediate graphs. 2. [6...

1(a)
     Graph of the function f(x) =
1
x
    
    1(b)
    let
g(x)=-1-
1
2
x
+
 and f(x) =
1
x
(given in 1(a))
            =  -1-f(x+2)
f(x+a) translates f(x) horizontally to the left by 2 unit
-f(x)  reflects f(x)over the x-axis
-1-f(x) translates f(x) vertically downwards by 1 unit
Hence the graph of the function 
g(x) = -1-
1
2
x
+
(using the graph of 1(a))

    
    2(a)
    For domain the function should not be undefined
So 4 – x2
¹
0
Þ
x
¹
2 and – 2
Also  2x+3
³
0
Þ

3
2
x
³-
Hence domain is
3
,0
2
éö
-
÷
ê
ëø
-{2}
Range:
 
    2(b)
    Domain:
The value of x2 – x – 6 should not be negative
x2 – x – 6
³
0
(x-3)(x+2)
³
0
Hence the domain is      R – (–2,3)
Range:
let y =
2
x – x – 6
y2 =  x2 – x – 6
x2 – x – 6 – y2

Þ
(
)
2
1146
2
y
x
±---
=

Þ
2
1254
2
y
x
±+
=
x is well defined for all real values of y but for same positive and negative values of y x remains same.
Hence the Range is set of non negative real number i.e. R – R-
    3(a).
     
(
)
2
lim
295
5
35
xx
x
x
--
®
-
Þ
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