Algebraic Fractions

Algebraic Fractions
When adding or subtracting algebraic fractions, the first thing to do is to put them onto a common denominator (by cross procreateing).

e.g. 1 + 4
(x + 1) (x + 6)

= 1(x + 6) + 4(x + 1)
(x + 1)(x + 6)

= x + 6 + 4x + 4
(x + 1)(x + 6)

= 5x + 10
(x + 1)(x + 6)
Solving equations
When solving equations containing algebraic fractions, first multiply both sides by a bite/expression which removes the fractions.

Example:
Solve 10 - 2 = 1
(x + 3) x

multiply both sides by x(x + 3):
10x(x + 3) - 2x(x + 3) = x(x + 3)
(x + 3) x

10x - 2(x + 3) = x² + 3x [after backsidecelling]
10x - 2x - 6 = x² + 3x
x² - 5x + 6 = 0
(x - 3)(x - 2) = 0
either x = 3 or x = 2

Functions
A agency is a rule which indicates an operation to perform.
e.g. if f(x) = x² + 3

f(2) = 2² + 3 = 7 (i.e. replace x with 2)

Functions can be graphed. For example, the graph of f(x) = 1/x is as follows:
This is the analogous graph as y = 1/x, although the y axis is f(x) instead of y.





Types of graphs
The graph of y = k/x (f(x) = k/x) is known as a hyperbola. Asymptotes are lines on a graph which the graph gets very close to, but neer touches. Therefore in the case of y = 1/x, the x and y axes are asymptotes.
Parabolas are graphs of the form y = ax² + bx + c (where a, b and c are numbers). They can be U shaped, when a is positive, or n shaped, when a is negative.

Graph Shifting
If you add 1 to f(x), this will fault the graph up 1 unit. i.e. f(x) + n shifts the graph upwards by n units.
f(x - 1) will shift the graph 1 unit to the right. i.e. f(x - n) shifts the graph n units to the right.
f(x + n) will shift the graph n units to the left.

Inverse Functions
The inverse consumption of y = 2x is y = ½x . The inverse of a function does the opposite of the function. To find the inverse of a function, follow the undermentioned procedures: let y =...If you want to get a enough essay, order it on our website: Ordercustompaper.com



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