Algebraic Functions 2

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.