Unit Aims

Functions

The aims of this unit are to explore the notion of function as a unifying theme in mathematics, and to apply functional methods to a variety of mathematical situations. 

It is expected that extensive use will be made of technology (especially GDC) in both the development and the application of this topic. 

The use of GeoGebra to complement the use of GDC is therefore very important.

Learning targets:

Powerpoint Presentation 

• ·       Concept of function: domain, range, image.
• ·       Composite functions
• ·       Inverse function.
• ·       Transformations of graphs: translations; stretches; reflections in the axes.
• ·       Vertical Translations: y= f(x) +b
• ·       Horizontal Translations y = f(x-a)
• ·       Horizontal and vertical translations by a vector.
• ·       Stretches: y= p f(x) ; y=f(x/q)
• ·       Reflections (in both axes): y=-f(x) ; y = f(-x)
• ·       The graph of the inverse function as the reflection in the line y=x of y=f(x)
• ·       The reciprocal function y=1/x
• ·       The quadratic function f(x) = ax^2+bx+c: its graph and y-intercept.
• ·       Axis of symmetry x= -b/2a
• ·       The form f(x)= a (x-h)^2 + k: vertex (h,k)
• ·       The form f(x)= (x-p)(x-q) : x intercepts (p,0), (q,0)
• ·       Exponential functions. f(x) = a^x (a>0)
• ·       Logarithmic functions.
• ·       The number e, e-based exponentials and logarithms (natural)
• ·       Trigonometric functions. The circular functions sin x, cos x and tan x: their domains and ranges; their periodic nature and their graphs.
• ·       Composite functions of the form f(x) = a sin (b (x+c)) +d.
• ·       Real-life examples.

For a more detailed plan of activities download this presentation.