State whether $y=1$ is a function or not.

Given \(f\left( x \right) = ax + b\), \(f\left( 0 \right) = 1\) \(f\left( 1 \right) = -1\) and \(f\left( 2 \right) = -1\), find \(a \) and \(b\).

Find the vertical asymptote(s) of \(f\left( x \right) = \dfrac{1}{{{x^2} – 1}}\).

Given \(f\left( x \right) = 2x – 1\), \(g\left( x \right) = x + 1\), \(\left( {f \circ f} \right)\left( 2 \right) = a\), \(\left( {g \circ f} \right)\left( 1 \right) = b\), \(\left( {f \circ g} \right)\left( c \right) = 3\) and \(\left( {g \circ g} \right)\left( d \right) = 1\) find the domain and range of \(a + b + c + d\).

Find the proper expression of the graph.

If  \(f\left( x \right) = 3{x^2} + 2\),   find  \(2f\left( {x + 2} \right) – 1\)  in simplest form.

Choose vector quantities.

Find the vector equation of the following diagram.

Given  \(\vec a = \left( {\begin{array}{*{20}{c}}
4\\
5
\end{array}} \right)\)  and   \(\vec b = \left( {\begin{array}{*{20}{c}}
{ – 2}\\
3
\end{array}} \right)\),   find   \(\left| {\vec a – \vec b} \right|\),   correcting to two significant figures.

Find the coordinates \(\left( {a,b,c} \right)\) of the point where the line with parametric equations \(x = -12 + 3t,{\rm{ }}y = – 12 – 3t\) and \(z = 4 + 2t\) meets the \(YOZ\) plane.