Exercise 1.3.5

Question

The graph of $f$ is given. Use it to graph the following functions.\begin{enumerate}[label=(\alph*)]
\item $y = f (2x)$,
\item $y=f(1/2\ x),$
\item $y = f (-x)$,
\item $y = -f(-x)$.
\end{enumerate}

Khagan Gulusoy · Accepted Answer

\begin{enumerate}[label=(\alph*)] \item we shrink the graph of $f$ horizontally by a factor of 2.\begin{figure}[H]\centering\begin{tikzpicture}[declare function={ f(\x) = (\x <= 1) * (\x+1) + (\x > 1 && \x <= 4) * (3-\x) + (\x > 4) * (-3 + 0.5*\x); }] \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} ] % Original function \addplot[domain=0:6, samples=100, color=red, dashed, ultra thick] {f(x)}; % f(2x) \addplot[domain=0:3, samples=100, color=violet, ultra thick] {f(2*x)}; \end{axis} \end{tikzpicture}\end{figure} \item \begin{figure}[H]\centering \begin{tikzpicture}[declare function={ f(\x) = (\x <= 1) * (\x+1) + (\x > 1 && \x <= 4) * (3-\x) + (\x > 4) * (-3 + 0.5*\x); }] \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} ] % Original function \addplot[domain=0:6, samples=100, color=red, dashed, ultra thick] {f(x)}; % f(1/2 x) \addplot[domain=0:12, samples=100, color=violet, ultra thick] {f(0.5*x)}; \end{axis} \end{tikzpicture} \end{figure} \item \begin{figure}[H]\centering \begin{tikzpicture}[declare function={ f(\x) = (\x <= 1) * (\x+1) + (\x > 1 && \x <= 4) * (3-\x) + (\x > 4) * (-3 + 0.5*\x); }] \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} ] % Original function \addplot[domain=0:6, samples=100, color=red, dashed, ultra thick] {f(x)}; % f(-x) \addplot[domain=0:-6, samples=100, color=violet, ultra thick] {f(-x)}; \end{axis} \end{tikzpicture} \end{figure} \item \begin{figure}[H]\centering \begin{tikzpicture}[declare function={ f(\x) = (\x <= 1) * (\x+1) + (\x > 1 && \x <= 4) * (3-\x) + (\x > 4) * (-3 + 0.5*\x); }] \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} ] % Original function \addplot[domain=0:6, samples=500, color=red, dashed, ultra thick] {f(x)}; % -f(-x) \addplot[domain=0:-6, samples=500, color=violet, ultra thick] {-f(-x)}; \end{axis} \end{tikzpicture} \end{figure} \end{enumerate}

Exercise 1.3.5

Answers

Comments

Exercise 1.3.5

Answers

Comments

Add answer