x 3 2 1 1
2
1
4
0
1
4
1
2
1 2 3
h(x) 1
3
1.Join the points with smooth curves.
2.What happens ifx= 0?
3.Explain why the graph consists of two separate curves.
4.What happens toh(x)as the value ofxbecomes very small or very large?
5.The domain ofh(x)isfx:x 2 R; x̸= 0g. Determine the range.
6.About which two lines is the graph symmetrical?SOLUTION
Step 1: Substitute values into the equation
h(x) =1
x
h( 3) =1
3
=
1
3
h( 2) =1
2
=
1
2
h( 1) =1
1
= 1
h(
1
2
)
=
1
^12
= 2
h(
1
4
)
=
1
^14
= 4
h(0) =1
0
=undefinedh(
1
4
)
=
1
1
4= 4
h(
1
2
)
=
1
1
2= 2
h(1) =1
1
= 1
h(2) =1
2
=
1
2
h(3) =1
3
=
1
3
x 3 2 1 1
2
1
4
0
1
4
1
2
1 2 3
h(x) 1
3
1
2
1 2 4 undefined 4 2 11
2
1
3
Step 2: Plot the points and join with two smooth curves
From the table we get the following points:
(
3; ^13
)
,
(
2; ^12
)
,( 1; 1),
(
^12 ; 2
)
,
(
^14 ; 4
)
,
( 1
4 ; 4
)
,
( 1
2 ; 2
)
,
(1; 1),
(
2;^12
)
,
(
3;^13
)
168 6.4. Hyperbolic functions