1AReciprocalGraphs

=The Graphs of Linear and Quadratic Functions and their Reciprocals.=

1A Sketch Graphs of y = ax m +bx -n + c where m = 1 or 2 and n = 1 or 2


 * You are expected to be able to graph y =ax + c ( linear ) and y = a(x+b) 2 ( quadratic ).


 * In this section we will look at the graphs produced by the reciprocal of those functions.


 * Reciprocal graphs usually have asymptotes.


 * A hyperbola is the reciprocal of a linear graph.


 * A truncus is the reciprocal of a quadratic graph with its turning point on the x-axis y = a(x+b) 2.


 * More complicated graphs are produced from the reciprocal of a quadratic graph where the turning point is not on the x-axis.
 * see **1B More Reciprocal Graphs**


 * We can sketch the graph of a combined function by sketching each part seperately and using Addition of Ordinates.


 * Some rational functions (fractions with algebra on numerator and denominator)
 * may need to be split into two or more terms
 * before sketching using Addition of Ordinates.


 * In all of these graphs, care must be taken to draw and label the asymptotes.
 * The line of the graph should approach but not touch the asymptote
 * and should not curve away from the asymptote.


 * Revise finding the location and nature of stationary points.

1B More Reciprocal Graphs


 * Sketch the reciprocal of a quadratic function with turning point not on the x-axis.

1F Sketch Graphs using partial fractions


 * Adding Hyperbolas can result in a line that crosses an asymptote.

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 * Partial fractions can be used to divide a more complicated rational function into the sum of simpler functions.
 * The function can then be sketched using addition of ordinates.