Exercise 1.2.9

Question

What do all members of the family of linear functions $f(x)= c - x$ have in common? Sketch several members of the family.

Khagan Gulusoy · Accepted Answer

The graphs of all elements $f_c$ of the given family of the linear functions $\{f_c\}_{c\in \mathbb{R}}$ are all parallel to each other because they all have slope $-1$.
ewline
Now we should sketch the graph of several members of the family described in the exercise. Let's take $c=1,$ $c=2$, $c=-2.$ 
\begin{figure}[H] \centering
    \begin{tikzpicture}
    \begin{axis}[axis lines=middle, xmin=-4, xmax=4, ymax=4, ymin=-4, xlabel={$x$}, ylabel={$y$}, x label style = {at={(ticklabel cs:0.9)},anchor=south,above=4.8mm}, y label style={anchor=north, above=3mm}]
         \addplot[domain=-4:4, samples=2, mark=none, color=blue, ultra thick] {1-x};
         \addplot[domain=-4:4, samples=2, mark=none, color=red, ultra thick] {2-x};
         \addplot[domain=-4:4, samples=2, mark=none, color=green!60!black, ultra thick] {-2-x};
    \end{axis}    
    \end{tikzpicture}
\end{figure}

Exercise 1.2.9

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Exercise 1.2.9

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