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Exponentials, SMB-005

Sketch the graph of  `y=3^x+2`, clearly labelling any asymptotes.  (3 marks)

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`y=3^x+2`

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1  & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 2 \frac{1}{9} & 2 \frac{1}{3} & 3 & 5 & 11\\
\hline
\end{array}

Exponentials, SMB-004

Sketch the graph of  `y=3(2^(-x))-1`  (3 marks)

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\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  & \ \ 3\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 5 & 2 & \frac{1}{2} & -\frac{1}{4} & -\frac{5}{8}\\
\hline
\end{array}

Exponential, SMB-003

By completing the table of values, sketch the graph of  `y=2^(-x)`  (3 marks)

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} \ \ x\ \  \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} \ \ y\ \  \rule[-1ex]{0pt}{0pt} &  &  & 1 &  & \\
\hline
\end{array}

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\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & 4 & 2 & 1 & \frac{1}{2} & \frac{1}{4}\\
\hline
\end{array}

Exponentials, SMB-002

  1. Complete the table of values below given  `y=2^x-1`  (2 marks)

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} &  & -\frac{1}{2} &  &  & 3\\
\hline
\end{array}

  1. Draw the graph of  `y=2^x-1`  on the Cartesian plane below.  (2 marks)


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i.   

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & -\frac{3}{4} & -\frac{1}{2} & 0 & 1 & 3\\
\hline
\end{array}

ii. 

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i.   

\begin{array} {|l|c|c|c|c|c|}
\hline
\rule{0pt}{2.5ex} x \rule[-1ex]{0pt}{0pt} & -2 & -1 & \ \ 0\ \  & \ \ 1\ \  & \ \ 2\ \  \\
\hline
\rule{0pt}{2.5ex} y \rule[-1ex]{0pt}{0pt} & -\frac{3}{4} & -\frac{1}{2} & 0 & 1 & 3\\
\hline
\end{array}

ii.