\chapter{Functions and graphs}
\section{Basic Functions and simple transformations}
Answer the questions in your own words.
\begin{enumerate}
\item
The picture below shows one of the basic functions discussed in this unit. What is its name?
\(\img{U1_10F4.jpg}{}{10em}{}\)
\item
The picture below shows one of the basic functions discussed in this unit. What is its equation?
\(\img{U1_10F7.jpg}{}{10em}{}\)
\item
What is the equation for the reciprocal function?
\item
What is the name of the function with equation \( y=x\)?
\item
What is the name of the function with equation \(y=x^2\)?
\item
The picture below shows one of the basic functions discussed in this unit. What is its name?
\(\img{U1_10F6.jpg}{}{10em}{}\)
\item
The picture below shows one of the basic functions discussed in this unit. What is its equation?
\(\img{U1_10F5.jpg}{}{10em}{}\)
\item
Suppose you are given the graph of a function \(f(x)\). How would you draw the graph of
the following:
\begin{enumerate}
\item \(f(x)+2\)
\item \(f(x+2)\)
\item \(f(x-3)\)
\item \(-f(x)\)
\item \(f(x)-5\)
\item \(f(-x)\)
\end{enumerate}
\item Suppose we need to draw the graph of \(f(x)=-(x+3)^2 +4\). Which of the following methods is correct?
\begin{enumerate}
\item Shift \(x^2\) left by 3, up by 4, and reflect across the \(x\)-axis.
\item Shift \(x^2\) up by 4, reflect across the \(x\)-axis, and shift left by 2.
\item Reflect \(x^2\) across the \(x\)-axis, shift left by 2 and up by 4.
\end{enumerate}
\end{enumerate}