The graph of the Periodic function y gx is given What is th

The graph of the Periodic function y = g(x) is given. What is the fundamental period of g? What is the amplitude of g? Find g(98)and g(-98). What is the fundamental period and amplitude of y = 2g(3x)? A closed box with a square base is made of material that costs $8 per m^2 for the top and bottom and $5 per m^2 for the sides. If the volume of the box is 12 m^3, express the cost of the box as a function of x.

Solution

8. A . From the graph look for distance between any two points which have repeated pattern on x axis.

The max, y point at x=0 is repeated again at x=5

So, Period = 5 units

B. Max amplitude can be seen is the maximum value in graph : 5 units

C g(98) = g(95 +3) = g(3) = -1 (i.e.function value at x=3)

g(-98)= g(-95 -3) = g(-3) = +1 (i.e.function value at x= -3)

D   y = 2g(3x)

Graph is horizontally shrink by 3 units and vertically stretched by 2 units

So, Fundamental Period = 5/3 units

Max Amplitude = 5*2 = 10 units

9. Volume of the box = x*x*h = x^2*h = 12 m^3

h = 12/x^2

Cost of top and bottom of box = $8 per m^2

Cost of sides of box = $5 per m^2

Cost of box = 2*x*h*8 + 2x*x*5

=16xh + 10x^2

Sustituting value of h =12/x^2

Cost of box = 16(12/x^2)x +10x^2 = 192/x +10x^2