Part A.
In this case, we need to find the difference between two consecutive output values. For instance,
[tex]f(-5)-f(-4)=-11-(-3)[/tex]
which gives
[tex]f(-5)-f(-4)=-11+3=-8[/tex]
If we choose another pair of consecutive values, we will have the same difference. Then, the answer for part A is -8
Part B.
In this case, we wiil choose any two inputs that are 2 units apart, for instance,
Then, the difference of the outputs is given by
[tex]f(-3)-f(-1)=5-21[/tex]
which gives
[tex]f(-3)-f(-1)=-16[/tex]
If we choose another pair of consecutive values, we will have the same difference. Then, the answer for part B is: -16
Part C.
Similarly to the previous cases, we need to find the difference between any inputs that are 3 units apart, for instance,
Then, the difference of the outputs is given by
[tex]\begin{gathered} f(-3)-f(0)=5-29 \\ f(-3)-f(0)=-24 \end{gathered}[/tex]
If we choose another pair of consecutive values, we will have the same difference. Then, the answer for part C is: -24
part D.
From the given results, the ratios are;
[tex]\begin{gathered} \text{part A:}\frac{\text{ }f(-5)-f(-4)}{-5-(-4)}=\frac{\text{ }f(-5)-f(-4)}{-1}=\frac{-8}{-1}=8 \\ \text{part B:}\frac{\text{ }f(-3)-f(-1)}{-3-(-1)}=\frac{\text{ }f(-3)-f(-1)}{-2}=\frac{-16}{-2}=8 \end{gathered}[/tex]
and
[tex]\text{part C:}\frac{\text{ }f(-3)-f(0)}{-3-0}=\frac{\text{-}24}{-3}=8[/tex]
As we can note the ratios are the same and equal to 8.
