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]
