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The table of data lists input-output values for a function. Complete parts a through c.

a) Is the change in the inputs, [tex]\( x \)[/tex], the same? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

\begin{tabular}{|c|c|}
\hline
[tex]$x$[/tex] & [tex]$y$[/tex] \\
\hline
-9 & -17 \\
-6 & -11 \\
-3 & -5 \\
0 & 1 \\
3 & 7 \\
6 & 13 \\
9 & 19 \\
\hline
\end{tabular}

A. Yes, and it is equal to [tex]\( 3 \)[/tex].

B. No.

b) Is the change in the outputs, [tex]\( y \)[/tex], the same? Select the correct choice below and, if necessary, fill in the answer box to complete your choice.

A. Yes, and it is equal to [tex]\(\square\)[/tex].

B. No.

Sagot :

GinnyAnswer
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].
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