a) f(-4)-f(-5)=-3- (-11)=-3+11=8
f(-2)-f(-3)=13-5= 8
f(0)-f(-1)=29-21= 8
f(2)-f(1)=45-37=8
f(3)-f(2)=53-45=8
all are 8
b) f(-3)-f(-5)= 5- (-11)= 5+11=16
f(-2)-f(-4)=13-(-3)=13+3=16
f(1)- f(-1)=37-21= 16
f(3)-f(1)=53-37=16
c) f(-2)-f(-5)=13-(-11)=13+11=24
f(-1)-f(-4)=21-(-3)=21+3=24
f(0)-f(-3)=29-5=24
f(1)-f(-2)=37-13=24
f(2)-f(-1)=45-21=24
d) The differences have the same ratio.
cause is a linear function f(x)=ax+b
f(x+3)-f(x)=a(x+3)+b-ax-b=ax+3a-ax=3a
f(x+2)-f(x)=2a
f(x+1)-f(x)=a
so it is the same for every x
