Arrange the absolute value functions from narrowest to widest with respect to the width of their graphs.

f (x) = 3/2|x-5|+5

f (x) = - 5|x+4|+4

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

f (x) = - 1/4|x-8|+3

f (x) = - 2/5|x+2|+5/2

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

f (x) = 3/4|x-1|+1

We have functions of the form:

f (x) = a[x+b]+c

[]: Absolute value

We can order in function of the absolute value of "a". The function narrowest is that with the biggest absolute value of "a".

1) a1=3/2=1.5→[a1]=[1.5]→[a1]=1.5

2) a2=-5→[a2]=[-5]→[a2]=5

3) a3=-2→[a3]=[-2]→[a3]=2

4) a4=-1/4=-0.25→[a4]=[-0.25]→[a4]=0.25

5) a5=-2/5=-0.4→[a5]=[-0.4]→[a5]=0.4

6) a6=1→[a6]=[1]→[a6]=1

7) a7=3/4=0.75→[a7]=[0.75]→[a7]=0.75

Ordering the values from the biggest to the smallest:

5 2 1.5 1 0.75 0.4 0.25

a2 a3 a1 a6 a7 a5 a4

Arrange the absolute value functions from narrowest to widest with respect to the width of their graphs. Answer:

1) f (x) = - 5[x+4]+4

2) f (x) = - 2[x-1]+1/2

3) f (x) = 3/2[x-5]+5

4) f (x) = [x+4]+7

5) f (x) = 3/4[x-1]+1

6) f (x) = - 2/5[x+2]+5/2

7) f (x) = - 1/4[x-8]+3