Reciprocal Graphs
Points of Intersection
● Coordinates of POI satisfy the equations of both curves/lines
● Solve equations simultaneously to get coordinates of POI
● Mark on graph when sketching
Proportional Relationships
● If y is directly proportional to x then the relationship between y and x can be
expressed as y ∝ x or y = kx where k is a constant
● Graphs of proportional relationships are straight lines through the origin
● If y is inversely proportional to x then the relationship between y and x can
be expressed as y ∝ 1x or y = kx where k is a constant
● This means that as one quantity increases, the other decreases
Graph Translations
y = f(x) + a
● This is a translation of the graph y = f(x) by a units parallel to the y-axis
y = f(x – a)
● This is a translation of the graph y = f(x) by a units parallel to the x-axis
y = f(x – a) + b
● This is a translation of the graph y = f(x) by a units parallel to the x-axis
and b units parallel to the y-axis
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Graph Stretches
y = af(x)
● This is a stretch by scale factor a parallel to the y-axis
y = f(ax)
● This is a stretch by scale factor a1 parallel to the x-axis
y = af(bx)
● This is a stretch by scale factor a parallel to the y-axis and by scale factor
b1 parallel to the x-axis
Reflections
y = – f(x)
● This is a reflection in the x-axis
y = f(- x)
● This is a reflection in the y-axis
● In some cases a reflection in the x-axis gives the same graph as a
reflection in the y-axis