# Discussion-Based Assessment

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) =
$\frac{}{}$

x

2

+

3

x

+

2

x

2

+

5

x

+

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.

PART 2: Over the course of this unit, what concept did you find the most challenging? What did you do to clarify this concept and further your learning? Please explain the concept and give at least one real world example that demonstrates the concept that you have selected.

Your response must be at least three paragraphs.

Units were:

 01.02 Introduction to Calculus 01.03 Review of Function Terminology and More 01.04 Graphing Calculators 01.05 Compositions and Transformations of Functions 01.06 Some Common Functions