Cubic Functions

1
Cubic Functions

• The basic graph of yx3 is shown left.
• For transformations we can consider the general
  equation
• ya(x-p)3q
• Where a is the multiplier affecting the steepness
  of the curve
• And p is the horizontal shift
• And q is the vertical shift

point of inflection
2
Graphs Equations (Cubic)

• Identify the point of inflection and note its
  co-ordinates (p, q)
• Find a such that
• When xp and yq

3
Hyperbolic Functions

• The graph of
• Is shown opposite.
• For transformations we can consider the general
  equation
• Where a is the steepness of the curve
• And p is the horizontal shift
• And q is the vertical shift
• Note that the graph approaches but does not cross
  the x and y axes
• These boundaries are called the asymptotes

4
Graphs Equations (Hyperbolic)

• Asymptotes should be identified first
• Horizontal asymptote xp
• Vertical asymptote yq
• Find a such that
• From the graph where p q have been identified.

5
Square Root

• The graph of yvx is shown below
• Transformation of this function can be considered
  from the general equation,
• Where a is the steepness of the curve
• And p is the horizontal shift
• And q is the vertical shift

6
Graphs Equations (Square Root)

• Locate the starting point to get p q
• Substitute these values to find the value of a