Exercise 1.3.8

Question

\begin{enumerate}[label=(\alph*)]
        \item How is the graph of $y = 1 +\sqrt{x}$ related to the graph of $y =\sqrt{x}$? Use your answer and Figure 4(a) to sketch the graph of $y = 1 +\sqrt{x}$.
        \item How is the graph of $y = 5 \sin \pi x $ related to the graph of $y = \sin x$? Use your answer and Figure 6 to sketch the graph of $y = 5 \sin \pi x .$
    \end{enumerate}

Khagan Gulusoy · Accepted Answer

\begin{enumerate}[label=(\alph*)]
        \item The graph of $y=1+\sqrt{x}$ is obtained by shifting the graph of $y=\sqrt{x}$ by $1$ unit upwards. We sketch the graph of $y=1+\sqrt{x}$ as follows:
        \begin{figure}[H] \centering
    \begin{tikzpicture}
    \begin{axis}[axis lines=left, xlabel={$x$}, ylabel={$y$}, x label style = {at={(ticklabel cs:0.9)},anchor=south,above=10mm}, y label style={anchor=north, above=3mm}]
         \addplot[domain=0:16, samples=50, mark=none, color=red, dashed, ultra thick] {sqrt(x)};
         \addplot[domain=0:16, samples=50, mark=none, color=blue, ultra thick] {1+sqrt(x)};
    \end{axis}    
    \end{tikzpicture}
    \end{figure}

\item To get the graph of $y=5\sin \pi x,$ we need to stretch the graph of $y=\sin x$ vertically by a factor of $5$ and then shrink it horizontally by a factor of $\pi.$ We get:
    \begin{figure}[H] \centering
    \begin{tikzpicture}
    \begin{axis}[axis lines=middle, xlabel={$x$}, ylabel={$y$}, x label style = {at={(ticklabel cs:0.9)},anchor=south,above=10mm}, y label style={anchor=north, above=3mm}]
         \addplot[domain=-8:8, samples=50, mark=none, color=red, dashed, ultra thick] {sin(deg(x)))};
         \addplot[domain=-8:8, samples=150, mark=none, color=blue, ultra thick] {5*sin(deg(pi*x))};
         \legend{$\sin x$, $5\sin(\pi x)$};
    \end{axis}    
    \end{tikzpicture}
    \end{figure}
    \end{enumerate}

Exercise 1.3.8

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Exercise 1.3.8

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