Exercise 16 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)
Reflections	In the x-axis y= - f(x)
	In the y-axis y=f( - x)
Vertical Stretch or Shrink	Vertical stretch, a>1 y= af(x)
	Vertical shrink, 0< a< 1 y= af(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)

Using the table, let's apply the first transformation, a reflection in the x-axis, by multiplying both sides of the equation by -1.

f(x)=|x|

MultEqn

LHS * ( -1)=RHS* ( -1)

-f(x)= -|x|

Next, we will apply the second transformation, a vertical stretch by a factor of 4, by multiplying both sides of the equation by 4.

- f(x)=-|x|

MultEqn

LHS * 4=RHS* 4

- 4f(x)=- 4|x|

After that we have translations: 7 units down and 1 unit to the right. We will apply them by subtracting 7 from both sides of the equation and substituting x- 1 for each x in the equation.

-4f(x)=-4|x|

SubEqn

LHS- 7=RHS- 7

-4f(x)- 7=-4|x|- 7

Substitute

x= x-1

-4f( x-1)-7=-4| x-1|-7

Finally, we can replace -4f(x-1)-7 with g(x) and complete the function rule. g(x)=-4|x-1|-7