Given the function [tex]\( p(x) = |x| - 3 \)[/tex], complete the table below:

[tex]\[
\begin{tabular}{|l|c|c|c|c|c|}
\hline
$x$ & -2 & -1 & 0 & 1 & 2 \\
\hline
$p(x)$ & 6 & 3 & 0 & 3 & 6 \\
\hline
\end{tabular}
\][/tex]



Answer :

We are given the function [tex]\( p(x) = |x| - 3 \)[/tex] and we need to calculate the values of [tex]\( p(x) \)[/tex] for [tex]\( x = -2, -1, 0, 1, 2 \)[/tex]. Let's go through each value step-by-step.

The absolute value function [tex]\( |x| \)[/tex] returns the non-negative value of [tex]\( x \)[/tex].

1. For [tex]\( x = -2 \)[/tex]:
[tex]\[ |x| = |-2| = 2 \][/tex]
Substituting into [tex]\( p(x) \)[/tex]:
[tex]\[ p(-2) = 2 - 3 = -1 \][/tex]

2. For [tex]\( x = -1 \)[/tex]:
[tex]\[ |x| = |-1| = 1 \][/tex]
Substituting into [tex]\( p(x) \)[/tex]:
[tex]\[ p(-1) = 1 - 3 = -2 \][/tex]

3. For [tex]\( x = 0 \)[/tex]:
[tex]\[ |x| = |0| = 0 \][/tex]
Substituting into [tex]\( p(x) \)[/tex]:
[tex]\[ p(0) = 0 - 3 = -3 \][/tex]

4. For [tex]\( x = 1 \)[/tex]:
[tex]\[ |x| = |1| = 1 \][/tex]
Substituting into [tex]\( p(x) \)[/tex]:
[tex]\[ p(1) = 1 - 3 = -2 \][/tex]

5. For [tex]\( x = 2 \)[/tex]:
[tex]\[ |x| = |2| = 2 \][/tex]
Substituting into [tex]\( p(x) \)[/tex]:
[tex]\[ p(2) = 2 - 3 = -1 \][/tex]

Summarizing these results, we get the values of [tex]\( p(x) \)[/tex] as follows:

[tex]\[ \begin{array}{|c|c|c|c|c|c|} \hline x & -2 & -1 & 0 & 1 & 2 \\ \hline p(x) & -1 & -2 & -3 & -2 & -1 \\ \hline \end{array} \][/tex]