Exercise 1.3.3

Question

The graph of $y = f (x)$ is given. Match each equation with its graph and give reasons for your choices.

Khagan Gulusoy · Accepted Answer

\begin{enumerate}[label=(\alph*)]
    \item The only graph that shows movement to the right is the 	extbf{third} one. Indeed, graph (3) has shifted four units to the right.
    \item By shifting the graph of the function $f$ upwards by three units, we obtain 	extbf{the graph (1)} that represents the function in (b).
    \item The graph of $1/3\ f(x)$ is the graph of $f$ that is shrunken vertically by a factor of $3.$ Thus, 	extbf{the graph (4)} illustrates the graph in (c).
    \item To graph $-f(x+4)$, we need to shift the graph of $f$ to the right by four units and then reflect it about the $x$-axis. The graph that represents these movements is 	extbf{the fifth graph}.
    \item To get the graph of $2f(x+6)$, first of all, we must shift the graph of $f$ to the right by six units. After we get the graph of $f(x+6),$ we must stretch it by a factor of $2$. The graph that represents such movements is 	extbf{the second graph}.
\end{enumerate}

Exercise 1.3.3

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Exercise 1.3.3

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