How can I Sketch the graphs of F(x) and f(x)

Question

The distributon function for the duration of a certain soap opera is F(x)=1-(16/x^2) , x> or equal 4 and F(x)=0 x<4 and the f(x)=32/x^3 , x> or equal 4 and f(x)=0 for x<4. How can I Sketch the graphs of F(x) and f(x) I find it so difficult,Could you please help me ?

Answer 1

I put an image of my sketches of these functions in my resources at:

  https://www.wyzant.com/resources/files/462325/sketching_1_4_x_2_and_32_x_3

  * You should be able to see this, let me know if there is a problem *

 

Here's the rough thoughts/process that I used in making the sketches:

F(X) = 1 - (4/x)2
- I rewrote the function a little as shown above.
- For F(4) we get 0 which is a continuation of the 0 for x<4.
- When x=8 we get 1 - 1/4 = 3/4
- When x = 12 we get 1 - 1/9 = 8/9
- As x continues getting larger F(X) will get closer to 1.
- If x = 4√2 (~ 5.7) then F(x) will be 1 - 1/2 = 1/2
- With all of this I choose the 0 to 20 x scale and the 0 to 1 F(x) scale.

f(x) = 32/x3
- For x<4 we have f(x) is 0
- at x=4 we get f(x) = 32/64 = 1/2 (or 0.5)
- at x=8 we get 32/512 ~ 0.063
- at x=12 ... ~ 0.02
- as x gets larger it gets closer to 0.
- Keeping the same x axis as for F(x), I made the f(x) axis go from 0 to 0.5
I also calculated f(6) ~ 0.15
and noted that f(x) would be 1/4 when x = 4*cuberoot(2) ~ 5 and added that point.

Note that this was my first sketch of these functions.
In general a first sketch may not be ideal and so I would adjust the scales, etc. based on how the first sketch looked to make a further sketch.

I hope this helps.