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
