Chapter 3, Problem 43SGR

To determine

Describe the transformation in given function.

Answer to Problem 43SGR

  $g\left(x\right)$ is shifted right 2 units and stretch vertically by a factor of 4units.

Explanation of Solution

Given information:

Parent function: $f\left(x\right)=x$

Transformed function: $g\left(x\right)=4\left(x-2\right)$

We have parent function $f\left(x\right)=x$ .

According to rule of transformation $g(x)=f(x-k),\text{ the graph of g(}x\text{) shifts right k units}\text{.}$

Also, if $g\left(x\right)=a\cdot f\left(x\right)\text{,}a>1\text{ then graph of g(}x)\text{ strecth vertically by a factor of }a.$

We could see $g\left(x\right)=f(x-2)$ that is $g\left(x\right)=x-2.$

Therefore, $g\left(x\right)$ is shifted 2 units right to the $f\left(x\right)$ .

Then, according to rule of transformation

  $g\left(x\right)=a\cdot f\left(x\right)\text{,}a>1\text{ then graph of g(}x)\text{ strecth vertically by a factor of a}$

Now we could see, $g\left(x\right)=4\cdot f\left(x-2\right)$ that is $g\left(x\right)=4(x-2).$

Therefore, the graph of $g\left(x\right)$ is shifted right 2 units and stretch vertically by a factor of 4 units.