AS-level Edexcel Pure Maths - Module 4: Graphs and Transformations|2023 LATEST UPDATE|GUARANTEED SUCCESS

Cubic A graph where the highest exponent is 3 Cubic function f(x) = ax³+bx²+cx+d Repeated root A function where at least 2 of the roots are equal. The turning point of the graph is on the x-axis E.g. y=(x-3)(x-2)² Point of inflection A function where all the roots are equal The graph flattens off on the x-axis E.g. y=(x-2)³ Sketching graphs with exponents Find the shape, roots, and y-intercept Mark any points of intersection with the axises - Shape is affected by the highest exponent, and whether a is ± f(x)=x³ f(x)=-x³ Quartic A graph where the highest exponent is 4 Quartic function f(x) = ax⁴+bx³+cx²+dx+e f(x)=x⁴ f(x)=-x⁴ Reciprocal A graph with 1 ÷ x. Has asymptotes Asymptotes A line which the graph approaches, but never reaches When a graph is translated, these are also translated f(x)=k÷x f(x)=-k÷x f(x)=k÷x² Point of intersection Where two graphs cross, or a graph crosses an axis f(x) = g(x) Finding points of intersection Set the functions equal to each other Solve Substitute the x values in to find y Transformation A change in the shape or position of a graph E.g. translation, reflection, enlargement, stretch Translation When a graph is shifted up / down / left / right y=f(x) ±b y=f(x±b) y=f(x)±b A translation of b in the y-axis +b moves right -b moves left