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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.

A. Yes, and it is equal to [tex]\square[/tex]
B. No

\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}

Sagot :

GinnyAnsweridn
To determine if the change in the inputs, [tex]\(x\)[/tex], is consistent, follow these steps:

1. Identify the [tex]\(x\)[/tex] values from the table:
[tex]\[ x = [-9, -6, -3, 0, 3, 6, 9] \][/tex]

2. Calculate the differences between consecutive [tex]\(x\)[/tex] values:
[tex]\[ -6 - (-9) = -6 + 9 = 3 \][/tex]
[tex]\[ -3 - (-6) = -3 + 6 = 3 \][/tex]
[tex]\[ 0 - (-3) = 0 + 3 = 3 \][/tex]
[tex]\[ 3 - 0 = 3 \][/tex]
[tex]\[ 6 - 3 = 3 \][/tex]
[tex]\[ 9 - 6 = 3 \][/tex]

3. Compare the differences to see if they are the same:
[tex]\[ [3, 3, 3, 3, 3, 3] \][/tex]
All the differences between consecutive [tex]\(x\)[/tex] values are [tex]\(3\)[/tex].

Therefore, the change in the inputs [tex]\(x\)[/tex] is the same, and it is equal to [tex]\(3\)[/tex].

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