Solution;
All the properties used to trace the graph are;
1)Domain.
Find the domain of the function and determine points of discontinuity.
Rewrite as follows;
For domain gaps,take the denominator to be equal to zero;
-(x+2)(x-2)=0
Therefore,the points of discontinuity are;
2) Intercepts.
For y -intercept,take x=0
y-intercept is (0,2)
The curve has no x-intercept.
3) Symmetry of the function.
The curve has neither axially symmetry nor point symmetry.
4)Intervals of increase or decrease.
5)Local maximum and minimum.
For (4) and (5),
The first derivative of f(x);
The second derivative is;
Looking for turning points;
Equate denominator of f'(x) to 0;
Hence the gaps are at;
x=2 or -2
If f'(x)=0;
Multiply both sides with the denominator;
16x=0
x=0
Turning points could be at x=0.
Substitute 0 into f''(x);
=1
Check if f'(x) changes sign to confirm;
Use -1 and 1;
There is change from positive to negative,hence there exist a turning point;
Substitute 0 into the f(x);
There is a minimum turning point at ;
(0,2)
Comments
Leave a comment