# Explain why a polynomial can have fewer x-intercepts than its number of roots.

1. A box is to be constructed from a sheet of cardboard that is 20 cm by 60 cm, by cutting out squares of length x by x from each corner and bending up the sides. What is the maximum volume this box could have?
2. Find the amplitude and period of y = –3cos(2x + 3).

Use your calculator to graph the function and state its symmetry.

Find the first positive x-intercept using your calculator’s zero function.

3. Find two functions f(x) and g(x) such that f[g(x)] = x but g[f(x)] does not equal x.
4. State the vertical, horizontal asymptotes and zeros of the rational function, f(x) = x2+3x+2×2+5x+4.

Why is there no zero at x = –1?

5. Give an example and explain why a polynomial can have fewer x-intercepts than its number of roots.

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