Chapter 3, Problem 44SGR

To determine

Describe the transformation in given function.

Answer to Problem 44SGR

  $g\left(x\right)$ is shifted left 4 units and compress vertically by a factor of 0.25units to the $f\left(x\right).$

Explanation of Solution

Given information:

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

Transformed function: $g\left(x\right)=0.25\left(x+4\right)$

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

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

We could see $g\left(x\right)=0.25\cdot f(x+4)$ that is $g\left(x\right)=0.25\left(x+4\right).$

Therefore, $g\left(x\right)$ is shifted 4 units left to $f\left(x\right)$ .

Then, according to rule of transformation

  $g\left(x\right)=a\cdot f\left(x\right)\text{,0< }a>1\text{ then graph of g(}x)\text{ compress vertically by a factor of a}$

Now we could see, $g\left(x\right)=0.25\cdot f\left(x\right)$

That is $g\left(x\right)=0.25\left(x+4\right).$

So, the graph of $g\left(x\right)$ is compress vertically by a factor of 0.25 units.

Therefore, the graph of $g\left(x\right)$ is shifted left 4 units and compress vertically by a factor of 0.25 units.