You should KNOW

1. That although the graph of polynomial function can have turning points, with more of them possible for higher degree polynomials, the large scale appearance of the graph (that is, as x approaches +/- infinity) is determined by the leading term.

2. The appearance of the graphs of y = axn for positive n as a guide to the large scale appearance of polynomial graphs (the Leading Coefficient Test).

3. The appearance of typical graphs for polynomials of degrees 1,2,3,4.

4. That a polynomial of degree n can have as many as n x-intercepts (corresponding to zeros of the polynomial) but may have fewer, and that the graph may cross or just touch the x-axis depending on the multiplicity of the corresponding zero.

You should be ABLE TO

1. Use information about x and y intercepts, symmetry, large scale behavior to make rough sketches of polynomial functions without the use of graphing calculator.

2. Use a graphing to get more accurate graphs and to estimate the zeros of polynomial functions by looking at x-intercepts using your graphing calculator.

3. Match geometric properties of the graph of a polynomial to its algebraic properties such as the degree, the leading coefficient, and the number of zeros.