Algebraic Functions

Check list:

The concept of a function, where a certain quantity (output value) uniquely depends on another quantity (input value). Work with relationships between variables using tables, graphs, words and formulae. Convert flexibly between these representations. Note that the graph defined by \(y=x\) should be known from Grade 9.
Point by point plotting of basic graphs defined by \(y=x^2\), \(y = \frac{1}{x}\) and \(y=b^x\), \(b>0\), \(b \ne 1\) to discover shape, domain (input values), range (output values), asymptotes, axes of symmetry, turning points and intercepts on the axes (where applicable).
Investigate the effect of \(a\) and \(q\) on the graphs defined by \(y=a.f(x)+q\), where \(f(x)=x\), \(f(x)=x^2\), \(f(x)=\frac{1}{x}\) and \(f(x)=b^x\), \(b>0\), \(b \ne 1\).
Point by point plotting of basic graphs defined by \(y = \sin \theta \), \(y=\cos\theta\) and \(y=\tan\theta\) for \(\theta \in \left[ {{0^o};{{360}^o}} \right]\).
Study the effect of \(a\) and \(q\) on the graphs defined by \(y=a\sin\theta+q\), \(y=a\cos\theta+q\); and \(y=a\tan\theta+q\) where \(a\), \(q \in \mathbb{Q}\) for \(\theta \in \left[ {{0^o};{{360}^o}} \right]\).
Sketch graphs, find the equations of given graphs and interpret graphs. Note: Sketching of the graphs must be based on the observation of number 3 and 5.

Learn the concepts:

Hello there Grade 10s. There is a part of me that is dreading this section. There is just so much content to cover and a small amount of time to get it done in. By the end of this section, you are going to be so sick of plotting functions! Plotting functions is a really important skill and when you master it, you will find the other, more complicated questions, far easier.

Grade 10s, you will work hard in this section. Make sure you are getting enough sleep and don't fall behind on your daily work!

Algebraic Functions:

Introduction to Functions

Videos from learn.mindset.co.za

Mind Action Series: Mathematics 10 Textbook & Workbook (2011)
Exercise 1 Page 126

Relevant sections in Everything Maths:

Functions in the real world

Still want to learn more? Try these links:

This website explains the concept of a function and the concepts domain and range of a function in the simplest possible way.

The Linear Function

Videos from learn.mindset.co.za

Mind Action Series: Mathematics 10 Textbook & Workbook (2011)
Exercise 2 Page 130
Exercise 3 Page 134
Exercise 4 Page 137
Exercise 5 Page 139
Exercise 6 Page 140
Exercise 7 Page 141

Relevant sections in Everything Maths: