Advanced Functions – Graphing techniques

This lesson comprises two (2) master classes focusing on:

• Function transformations
• Sketching functions

Content:

MA-F2

• Apply transformations to sketch functions of the form \( y=kf(a(x+b))+c \), where \( f(x) \) is a polynomial, reciprocal, absolute value, exponential or logarithmic function and a, b, c and k are constants
  • examine translations and the graphs of \( y=f(x)+c \) and \( y=f(x+b) \) using technology
  • examine dilations and the graphs of \( y=kf(x) \) and \( y=f(ax) \) using technology
  • recognise that the order in which transformations are applied is important in the construction of the resulting function or graph
• Use graphical methods with supporting algebraic working to solve a variety of practical problems involving any of the functions within the scope of this syllabus, in both real-life and abstract contexts
  • select and use an appropriate method to graph a given function, including finding intercepts, considering the sign of \( f(x) \) and using symmetry
  • determine asymptotes and discontinuities where appropriate (vertical and horizontal asymptotes only) 
  • determine the number of solutions of an equation by considering appropriate graphs
  • solve linear and quadratic inequalities by sketching appropriate graphs