Answer :

GinnyAnswer
To solve for the values of the function [tex]\( f(x) = x^2 - 3 \)[/tex] over the domain [tex]\( D = \{-3, -2, -1, 0, 1, 2, 3\} \)[/tex], we will evaluate the function at each value in the domain step-by-step.

1. Evaluate [tex]\( f(-3) \)[/tex]:
[tex]\[ f(-3) = (-3)^2 - 3 = 9 - 3 = 6 \][/tex]

2. Evaluate [tex]\( f(-2) \)[/tex]:
[tex]\[ f(-2) = (-2)^2 - 3 = 4 - 3 = 1 \][/tex]

3. Evaluate [tex]\( f(-1) \)[/tex]:
[tex]\[ f(-1) = (-1)^2 - 3 = 1 - 3 = -2 \][/tex]

4. Evaluate [tex]\( f(0) \)[/tex]:
[tex]\[ f(0) = 0^2 - 3 = 0 - 3 = -3 \][/tex]

5. Evaluate [tex]\( f(1) \)[/tex]:
[tex]\[ f(1) = 1^2 - 3 = 1 - 3 = -2 \][/tex]

6. Evaluate [tex]\( f(2) \)[/tex]:
[tex]\[ f(2) = 2^2 - 3 = 4 - 3 = 1 \][/tex]

7. Evaluate [tex]\( f(3) \)[/tex]:
[tex]\[ f(3) = 3^2 - 3 = 9 - 3 = 6 \][/tex]

Now, let’s compile all the results:

[tex]\[ \begin{align*} f(-3) & = 6, \\ f(-2) & = 1, \\ f(-1) & = -2, \\ f(0) & = -3, \\ f(1) & = -2, \\ f(2) & = 1, \\ f(3) & = 6. \end{align*} \][/tex]

So, the list of the values of [tex]\( f(x) \)[/tex] for each [tex]\( x \)[/tex] in the domain [tex]\( D \)[/tex] is:

[tex]\[ [6, 1, -2, -3, -2, 1, 6] \][/tex]

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