Let's solve the problem step-by-step by examining the changes in the input values [tex]\(x\)[/tex] and output values [tex]\(y\)[/tex].
### Step 1: Calculate the Changes in Input Values [tex]\(x\)[/tex]
First, we'll check if the change between consecutive [tex]\(x\)[/tex] values is the same. Given [tex]\(x\)[/tex] values are [tex]\(-9, -6, -3, 0, 3, 6, 9\)[/tex].
We calculate the differences between consecutive [tex]\(x\)[/tex] values:
- [tex]\(x_2 - x_1 = -6 - (-9) = 3\)[/tex]
- [tex]\(x_3 - x_2 = -3 - (-6) = 3\)[/tex]
- [tex]\(x_4 - x_3 = 0 - (-3) = 3\)[/tex]
- [tex]\(x_5 - x_4 = 3 - 0 = 3\)[/tex]
- [tex]\(x_6 - x_5 = 6 - 3 = 3\)[/tex]
- [tex]\(x_7 - x_6 = 9 - 6 = 3\)[/tex]
All these differences are the same and equal to 3.
So, the change in inputs [tex]\(x\)[/tex] is the same, and it is equal to 3.
Answer for part a:
A. Yes, and it is equal to [tex]\(3\)[/tex].
### Step 2: Calculate the Changes in Output Values [tex]\(y\)[/tex]
Next, we'll check if the change between consecutive [tex]\(y\)[/tex] values is the same. Given [tex]\(y\)[/tex] values are [tex]\(-17, -11, -5, 1, 7, 13, 19\)[/tex].
We calculate the differences between consecutive [tex]\(y\)[/tex] values:
- [tex]\(y_2 - y_1 = -11 - (-17) = 6\)[/tex]
- [tex]\(y_3 - y_2 = -5 - (-11) = 6\)[/tex]
- [tex]\(y_4 - y_3 = 1 - (-5) = 6\)[/tex]
- [tex]\(y_5 - y_4 = 7 - 1 = 6\)[/tex]
- [tex]\(y_6 - y_5 = 13 - 7 = 6\)[/tex]
- [tex]\(y_7 - y_6 = 19 - 13 = 6\)[/tex]
All these differences are the same and equal to 6.
So, the change in outputs [tex]\(y\)[/tex] is the same, and it is equal to 6.
Answer for part b:
A. Yes, and it is equal to [tex]\(6\)[/tex].
