\chapter{Functions and graphs}
\section{Basic Functions and simple transformations}
Answer the questions in your own words.
\begin{enumerate}
\item
How are the graphs of the following functions obtained from the graph of \(f(x)\)?
\[
\begin{array}{cccc}
\mbox{a. } 3f(x) & \mbox{b. } f(3x) & \mbox{c. } \displaystyle{\frac{1}{3}f(x)}
& \mbox{d. } \displaystyle{f\left(\frac{x}{3}\right)}
\end{array}
\]
\item
Describe in words how the graph of the function \(2f(x-1)-3\) is obtained from the graph of \(f(x)\)
\item
Suppose \(f(x)\) is stretched horizontally by \(a\). What can you say about the resulting
vertical stretching or compression?
\item
Suppose \(P=(3,-1)\) is the vertex of a transformed square function, and \(Q=(6,10)\) is another
point on the graph.
What is the vertical stretching or compression for the transformed graph?
\item
Suppose \(P\) and \(Q\) are as in the previous question,
but the parent function is the absolute value function. What is the vertical stretching or compression?
\item
Suppose now the parent function is the square root function, and you have worked out from
the two points \(P\) and \(Q\) that there is a vertical stretch by 4. What is the corresponding
horizontal compression?
\item
The graph of the parent cube function is compressed horizontally by 3, then it is reflected across
the \(x\)-axis, then it is shifted down by 5. What is the equation of the transformed
graph?
\end{enumerate}