Quantitative Analysis For Business and Economics Examples Covered in Lectures

2011

WARNING! 1. These examples were given as part of a Lecture. To look at them outside of their original context would be reckless. Be sure to understand these examples in the context of the lecture material. 2. Since they are Lecture examples, they are subject to the constraints of lectures: they do not aim to illustrate all the techniques that you are expected to master in the course. 3. Lecture examples intend to demonstrate a particular application of a method. You will not be testing your ability to recognise which kind of question you have before you by simply reading these through (they are often labelled!). Life does not usually come in such neat packages. It is recommended that you construct your own tests from textbook and tutorial problems to enhance your problem recognition and solution skills. Happy studying!

Lecture 1

1.1 Q: A linear function Consider what is meant by the simple linear function f (x) = 1 + 0.5x. A: “ef-of-x is equal to 1 plus 0.5 times x.” Each x value put into function f will give exactly one f (x) value. If we are dealing with continuous inputs (x can take any value between 0 and 5 say), then we normally draw a line to represent the functional relationship between f (x) and x.

6 5 4

1.2 Q: A:

Dependent, Independent Identify the dependent and independent terms, and the value and argument of the function H(a, b, c) = a2 + 2b + 3. • H depends on a and b (the independent variables); • H is the value, whilst a and b are the arguments.

1.3 Q: A:

Find the domain of the function, y(x) = Factorising gives, y(x) = 2 , (x − 1)(x + 4)

2 . x2 +3x−4

f (x)

3 2 1 0

*

0

*

1

*

2

*

*

*

which implies, x = 1 or -4. Hence, the domain of y is the Real

3 4 5 6

x

numbers except 1, -4.

1

1.4 Q: A:

Combining functions Suppose f (x) = 2x2 −3x−2 and g(x) = x − 2, and let h(x) = f (x), then show