Exercise 17 Page 20

To write the function rule g(x), let's look at possible transformations. Then we can more clearly decide which operations should be used to apply the desired transformations to the parent function.

Transformations of f(x)
Vertical Translations	Translation up k units, k>0 y=f(x)+ k
	Translation down k units, k>0 y=f(x)- k
Horizontal Translations	Translation right h units, h>0 y=f(x- h)
	Translation left h units, h>0 y=f(x+ h)
Vertical Stretch or Shrink	Vertical stretch, a>1 y= af(x)
	Vertical shrink, 0< a< 1 y= af(x)

First we have translations: 1 unit down and 2 units to the left. We will apply them by subtracting 1 from both sides of the equation and substituting x+ 2 for each x in the equation.

f(x)=|x|

SubEqn

LHS- 1=RHS- 1

f(x)- 1=|x|- 1

Substitute

x= x+2

f( x+2)-1=| x+2|-1

Next, we will apply the a vertical shrink by a factor of 12, by multiplying both sides of the equation by 12.

f(x+2)-1=|x+2|-1

MultEqn

LHS * 1/2=RHS* 1/2

1/2(f(x+2)-1)= 1/2(|x+2|-1)

Distr

Distribute 1/2

1/2f(x+2)-1/2=1/2|x+2|-1/2

Finally, we can replace 12f(x+2)- 12 with g(x) and complete the function rule. g(x)=1/2|x+2|-1/2