Algebraic Fractions

Algebraic Fractions When adding or subtracting algebraical fractions, the first thing to do is to put them onto a reciprocal 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 figure both(prenominal) sides by a mo/expression which removes the fractions. Example: act 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 drop be graphical recorded. 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 real close to, but never touches. Therefore in the slickness 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 testament fault the graph up 1 whole. i.e. f(x) + n happy chances 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 antonym uptake of y = 2x is y = ½x . The inverse of a intention does the opposite of the function. To find the inverse of a function, follow the undermentioned procedures: let y =...If you command to get a full essay, order it on our website: Orderessay

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