Chapter 1 - Functions - 1.2 Representing Functions - 1.2 Exercises - Page 26: 85

a) See table b) See graph c) $n=10$

We are given the factorial function: $f(n)=n!=n\cdot (n-1)\cdot (n-2)\cdot....\cdot 3\cdot 2\cdot 1$ a) Build a table of the factorial function for $n=1,2,3,4,5$. b) Plot the points and join them by a smooth curve. c) Compute $f(n)$ until we reach $10^6$: $f(7)=7!=5040$ $f(8)=8!=40320$ $f(9)=9!=362880$ $f(10)=10!=3628800=3.6\cdot 10^6$ Therefore the least value for which $n!>10^6$ is $n=10$.