**Solution:**

X 4 8 12 16 20

F(x) 11 25 16 9 31

A function is said to be increasing if ,

As you can see from the table given as x increases , f(x) increases as well as decreases.

So it is increasing as well as decreasing function.

Now plotting the graph on two dimensional coordinate plane and drawn perpendicular from these points on X axis.

Equation of line joining two points

Equation of line joining two points (4,11) and (8,25) is

4(y-11)=14(x-4)

4 y -44 = 14 x -56

4 y = 14 x -12

y= --------(1)

Area under line (1) is

Equation of line joining (8,25) and (12,16) is

4(y-25 )= -9(x-8)

4 y - 100= -9 x + 72

4 y = -9 x + 172

y = --------(2)

Area under line 2 is

Equation of line joining (12,16) and (16,9) is

-4(y-16) = 7(x-12)

-4 y + 64= 7 x -84

-4 y = 7 x -148

y = -----------(3)

Area under the line 3 is

Equation of line joining (16,9) and (20,31) is

4(y-9) = 22(x-16)

4 y - 36 = 22 x - 352

4 y = 22 x - 316

y= ---------(4)

Area under the line 4 is

Total Area = Area under the line (1+2+3+4)

=

= 72 +82+50+80

= 284 square units

You can find area using the formual of area of trapezoid which is = [Sum of parallel sides]× [perpendicular distance between them]