Factorial Notation?

Question

Consider the functions f(x)=x^2 , g(x)=x , h(x)=x!
where {0≤ x ≤10, x E* I}

a) make a table of values for f(x), g(x), h(x)

b) which of the three functions grows the fastest?

* the E above is actaully the math symbol that is 7th in this list :http://spot.pcc.edu/~ssimonds/thisandthat/Image2345.gif

Answer 1

f(x)=x^2
f(1)=1^2=1
f(2)=2^2=4
f(3)=3^2=9
:
:
f(10)=10^2=100


g(x)=x
g(1)=1
g(2)=2
:
:
g(10)=10

h(x)=x!
h(1)=1!=1
h(2)=2!=1x2=2
h(3)=3!=1x2x3=6
h(4)=4!=1x2x3x4=24
:
:
h(10)=10!=1x2x3x4x5x6x7x8x9x10= 3628800

Factorials always grow quickly :)

Answer 2

I'm not sure about what the E-symbol means, but I'll do a table from 0 to 10:

x - f(x), g(x), h(x)
0 - 0, 0, 0
1 - 1, 1, 1
2 - 4, 2, 2
3 - 9, 3, 6
4 - 16, 4, 24
5 - 25, 5, 120
6 - 36, 6, 720
7 - 49, 7, 5040
8 - 64, 8, 40320
9 - 81, 9, 362880
10 - 100, 10, 3628800

Answer 3

Use a calculator. By the time x = 4 you'll see that x! grows the fastest.