Author: gjooheng

H2 maths tutor

Solving function f = f inverse

f1

1

f2

2

f3

3

Tip: If we are not sure whether f and f inverse intersect, we can use the graphing calculator TI 84 plus to plot function f and f inverse together.

Y1 = “function f”

DrawInv Y1 (2nd prgm 8, alpha trace, Y1)

Challenging Normal Distribution problem 2

normal

See Square root of x squared

Juggling: shortcut to long division

Juggling is a shortcut to long division, especially in the case where the degree of the numerator is the same as the denominator. In H2 math, juggling is a useful technique in finding the asymptote of graphs and integration.

juggling

Triangular permutations

A group of 9 people sits at a triangular table, which is equilateral, with 3 persons at each side of the table. Find the number of different possible arrangements.

Solution

The 3 arrangements below are considered the same

triangle

Therefore, number of different possible arrangements = 9! / 3

Finding suitable replacement to solve new inequalities

ineq1

ineq2

ineq3

Graph transformation of oblique asymptote

Many students have difficulty with the graph transformation of oblique asymptote. Consider the oblique asymptote y = x-1 (red line)

oblique

i) y= 1/ f(x)

f(x) approaches infinity as x approaches infinity. 1 divided by infinity is 0.

Hence oblique asymptote y=x-1 becomes horizontal asymptote y= 0

For y= 1/ f(x), any oblique asymptote y=ax+b in f(x) will become horizontal asymptote y= 0 

ii) y= f ‘ (x)

The gradient of y= x-1 is 1. Hence oblique asymptote y=x-1 becomes horizontal asymptote y= 1

For y= f ‘ (x), any oblique asymptote y=ax+b in f(x) will become horizontal asymptote y= a

iii) y= f(2x+1)

Let original asymptote be f(x) = x-1

Therefore, f(2x+1) = (2x+1)-1 = 2x

Hence oblique asymptote y = x-1 is transformed to y=2x.

This method can be applied to any oblique asymptote.