Question

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

Answer 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