Check list:

  1. Revise the effect of the parameters \(a\) and \(q\) and investigate the effect of \(p\) on the graphs of the functions defined by: 
    1.1.  \(y = f\left( x \right) = a{\left( {x + p} \right)^2} + q\)
    1.2.  \(y = f\left( x \right) = \frac{a}{{x + p}} + q\)
    1.3.  \(y = f\left( x \right) = a{b^{x + p}} + q\) where \(b > 0\,,\quad b \ne 1\).
  2. Investigate numerically the average gradient between two points on a curve and develop an intuitive understanding of the concept of the gradient of a curve at a point.
  3. Investigate the effect of the parameter \(k\) on the graphs of the functions defined by \(y = \sin \left( {kx} \right)\), \(y = \cos \left( {kx} \right)\) and \(y = \tan \left( {kx} \right)\).
  4. Investigate the effect of the parameter \(p\) on the graphs of the functions defined by \(y = \sin \left( {x + p} \right)\), \(y = \cos \left( {x + p} \right)\) and \(y = \tan \left( {x + p} \right)\).
  5. Draw sketch graphs defined by:
    \(y = a\sin k\left( {x + p} \right)\) 
    \(y = a\cos k\left( {x + p} \right)\) and
    \(y = a\tan k\left( {x + p} \right)\) at most two parameters at a time.

Learn the concepts:

Well, Grade 11s, we're finally at the last section for this term and it's a big one. I really like functions. Like conventional algebra (solving equations, factorising, etc) it's easy to do when you know the steps. In other words, you can get full marks for this section IF you practice, and practice, and practice. Work hard in these next 4 weeks!

Algebraic Functions:

Recapping Grade 10 Algebraic Functions

The Quadratic Function    \(y = a{\left( {x + p} \right)^2} + q\)
Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 2 Page 94 
Exercise 3 Page 98 
Relevant sections in Everything Maths:
Still want to learn more? Try these links:

The Hyperbolic Function    \(y = f\left( x \right) = \frac{a}{{x + p}} + q\)
Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths:Still want to learn more? Try these links:

The Exponential Function    \(y = f\left( x \right) = a{b^{x + p}} + q\)  where  \(b > 0\,,\quad b \ne 1\)
Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths:Still want to learn more? Try these links:

Mixed Algebraic Functions
Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths:Still want to learn more? Try these links:

Trigonometric Functions:

Recapping Grade 10 Trigonometric Functions
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Videos from learn.mindset.co.za

The Sine Function    \(y = a\sin k\left( {x + p} \right)\)
Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths:

The Cosine Function    \(y = a\cos k\left( {x + p} \right)\)
Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths:

The Tangent Function    \(y = a\tan k\left( {x + p} \right)\)     
Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths:

Practice the concepts:

Check out that sexy teacher!
Videos from learn.mindset.co.za
Mind Action Series: Mathematics 11 Textbook & Workbook (2012):
Exercise 
Relevant sections in Everything Maths: