Proportional Relationships Proportional relationships Proportional relationships describe a proportional connection between two variables This can happen in two ways Both direct and inverse proport...
Solving Equations Graphically Solving (simultaneous) equations graphically This is a way to solve simultaneous equations (see Simultaneous Equations) Coordinates of the intersections are the soluti...
Reciprocal Graphs - Sketching What are reciprocal graphs? The second one of these is always positive More reciprocal graphs You also need to recognise graphs where the numerator is not one The sign...
Sketching Polynomials Sketching the graph of a polynomial Remember a polynomial is any finite function with non-negative indices, that could mean a quadratic, cubic, quartic or higher power When as...
Inverse Functions Inverse functions An inverse function is the opposite to the original function It is denoted by f-1(x) An inverse only exists for one-to-one functions Graphs of inverse functions ...
Composite Functions What is a composite function? A composite function is where one function is applied after another function The ‘output’ of one function will be the ‘input’ of the next one Somet...
Language of Functions Language of functions The language of functions has many keywords associated with it that need to be understood What are mappings? A mapping takes an ‘input’ from one set of v...
Inequalities on Graphs Inequalities on graphs Inequalities can be represented on graphs by shaded regions and dotted or solid lines These inequalities have two variables, x and y Several inequaliti...
Quadratic Inequalities Quadratic inequalities Similar to quadratic equations Sketching a quadratic graph is essential Can involve the discriminant or applications in mechanics and statistics How do...
