Below is sample of QUANTITATIVE ANALYSIS STUDY NOTES as per July 2021 syllabus
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Functions are often representatives of real phenomena or events. Functions therefore are models. Obtaining a function to act as a model is commonly the key to understanding business in many areas.
Functions may be represented by formulae. There are a number of common ways in which functions are presented and used. We shall consider functions given by formulae, since this provides a natural context for explaining how a function works.
- Functions of one variable
If you get a job that pays Ksh 200 per hour, the amount of money M that you earn depends on the number of hours (h) that you work, and the relationship is given by a simple function:
The formula M=200h shows that the money M that you earn depends on the number of hours worked. We say that M is a function of h.
In this context, h is a variable whose value we may not know until the end of the week. Once the value of h is known, the formula M=200h can be used to calculate the value of M. To emphasise that M is a function of h, it is common to write M=M(h),so that M(h)=700h.
if you work 30 hours, then the function M(30) is the money you would earn. To calculate the amount earned, you need to replace the formula by 30. Thus, M = M(30) = 700×30 = sh. 21,000.
- It is important to remember that h is measured in hours and M is measured given is Kenya shillings. The function/formula is not useful unless you state in words the units you are using.
- We would also use different letters or symbols for the variables. Whatever letter/symbol used, it is critical that you explain in word what they mean.
We normally write functions as f(x) and read as “function f of x”. We could use other letters such as g, p, H or h and write the function of x as g(x), p(x), H(x) or h(x).
Given f(x) = 3x +5, the value of this function f(x) when x=0 is written as f(0). The values are obtained by substituting.
- a) Given f(x) = 3x + 5, find i) f(0), ii) f(2) and iii) f(-2).
- b) Given that h(x) =2×2 +5x +3, find i) h(0). ii) h(-2) and iii) h(3).
- c) Given that G(t) = 2 +3t – 5t2 +t3, find i) g(-1) and g(2).
- d) If h(x) = 5 – 2x, find the value of x for which the function is zero.
- a) i) f(0) =3(0) + 5 = 0 + 5 = 5
- ii) f(2) =3(2)+5 = 6 + 5=11
iii) f(-2) = 3(-2) + 5 = -6 +5 = -1
- b) i) h(0) = 2(0)2+ 5(0)+3 = 3
- ii) h(-2) = 2(-2)2 + 5(-2) +3 =1
iii) h(3) = 2(3)2+ 5(3)+3 = 36
- c) i) G(-1) = 2+3(-1)-5(-1)2-2(-1)3 = -4
- ii) G(2) = 2+3(2) – 5(2)2 – 2(2)3 = -28
- d) h(x) = 5-2x = 0
-2x = – 5 x = 2.5
Example 2. 3
- a) If f(x) = 5x -3. find f(x+2).
- b) If y = g(x) = 3x – 7. find g(y) in terms of x.