We described the graphs of , , , , for , in terms of the the graph of (assuming we know everything about the graph of ).

We defined the *quadratic function* and what a *root* of a function is. We derived the familiar equation for the roots of the quadratic, and explained how the term determines the nature of the roots. We noted the inherent symmetry of the quadratic, and how if we know the graph of we have a rough idea of the shape of a quadratic by looking at the sign of the squared term.

We defined a *polynomial* function – and noted that the quadratic function is an example of one. We wrote down the *Factor Theorem* (without proof – a proof is given on this webpage). We wrote down the *Fundamental Theorem of Algebra* (whose proof is beyond the scope of the course). We defined a *rational function* and described a method of solving inequalities involving rational functions (although we made an assumption about polynomials – namely that they are *continuous* – this assumption will be shown to be true in the next few weeks).

We defined the *absolute value function* and proved some of its properties. Finally we described the sets and .

**Exercises**

Q.4-6 and 7(i) from http://euclid.ucc.ie/pages/staff/wills/teaching/ms2001/exercise1.pdf

Q. 1-2 from Problems

From class:

Let , . Prove that

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