## 2011-2012

Problem 1: Limits

Describe or draw a function, *f*(*x*), with the following characteristics:

*f*(*x*) has domain (–∞,8)*f*(*x*) has range (–∞,9)*f*(4) = 0;*f*(5) = 0;*f*(7) = 0- The limit, as
*x*approaches –∞, of*f*(*x*) equals 9 - The limit, as
*x*approaches 8 from the left, of*f*(*x*) equals –∞ *f*(–1) =*f*(–3);*f*(–1) >*f*(–2)*f*(1) = 1- The limit, as
*x*approaches 1, of*f*(*x*) is 4

### One Solution (others possible but similar):