Introduction To Precalculus

       
           

Pre calculus introduction involves sets, real and complex numbers, solving inequalities and equations, functions and their properties, composite, polynomial, rational, and trigonometric functions, sequences and series, binomial theorem, vectors, parametric equations, polar coordinates, matrix and their determinants, etc. Let’s see some formal rules used in precalculus. First we will see, how to replace one set of symbols with other. In arithmetic, symbols '3 + 3' is replaced by symbol ‘6’ and in algebra 'x + (−x)' replaced with '0.'

The following rule can be used to get introduction to precalculus.
p + q = r implies p = r − q.
p = p shows identity. If p = q then q = p shows symmetry.        
If p =q and q = r then p = r shows condition of transitivity. Commutative rules is p + q = q + p and p * q = q * p.

Let’s see an example of a line to understand precalculus problems. We know that, line through  a point (x (0), y (0)) with slope ‘m’ is represented by following equation y – y (0) = m (x – x (0)).
y = m x + c where ‘m’ is slope and ‘c’ is y intercept. To find an equation of line which passes through  point (3, -6) and slope (m) is 4.
Then y - (-6) = 4 (x - 3) Or y + 6 = 4x – 12
And y = 4x – 6
Since y = 4x + c then at x = 3 and y = -6, the value of c
- 6 = 4 * 3 + c
c = -18.

Math Topics