Chapter 1.2, Problem 2E

To determine

To find: The odd one out of the given options.

Answer to Problem 2E

The option “stretch the graph of $f(x)=x+3$ vertically be a factor of $2$ ” doesn’t belong to the other three.

Explanation of Solution

Given information: Four different options mentioning functions and transformation procedure are given.

Carrying out translation of $2units$ upward on the graph of $f(x)=2x+3$ ,

  $\begin{array}{l}g(x)=f(x)+2\\ \\ g(x)=2x+5\end{array}$

Shrinking the graph of $f(x)=x+5$ horizontally by a factor of $\frac{1}{2}$ ,

  $\begin{array}{l}g(x)=f(2x)\\ \\ g(x)=2x+5\end{array}$

Stretching the graph of $f(x)=x+3$ vertically by a factor of $2$ ,

  $\begin{array}{l}g(x)=2(x+3)\\ \\ g(x)=2x+6\end{array}$

Translating the graph of $f(x)=2x+3$ left $1unit$ ,

  $\begin{array}{l}g(x)=f(x+1)\\ \\ g(x)=2(x+1)+3\\ \\ g(x)=2x+5\end{array}$

  $f(x)=x+3$ is different, as after transformation, it becomes $2x+6$ .

Thus, the option “stretch the graph of $f(x)=x+3$ vertically be a factor of $2$ ” doesn’t belong to the other three.