A set of weights includes a 4 lb barbell and 6 pairs of weight plates. Each pair of plates weighs 20 lb. If [tex]$x$[/tex] pairs of plates are added, the total weight of the barbell and plates in pounds can be represented by the function [tex]f(x) = 20x + 4[/tex].

What is the range of the function for this situation?

A. [tex]\{4, 24, 44, 64, 84, 104, 124\}[/tex]
B. [tex]\{4, 44, 84, 124\}[/tex]
C. [tex]\{0, 2, 4, 6\}[/tex]
D. [tex]\{0, 1, 2, 3, 4, 5, 6\}[/tex]

To solve the problem, we need to find the range of the function [tex]$ f(x) = 20x + 4 $[/tex], where [tex]$ x $[/tex] represents the number of pairs of weight plates added to a 4 lb barbell.

Here are the steps to find the range:

1. Identify the Variables and Function:
- The barbell itself weighs 4 lb.
- Each pair of weight plates weighs 20 lb.
- The function [tex]$ f(x) = 20x + 4 $[/tex] represents the total weight where [tex]$ x $[/tex] is the number of pairs of plates.

2. Determine Possible Values for [tex]$ x $[/tex]:
- Since there are 6 pairs of weight plates, [tex]$ x $[/tex] can take on values from 0 to 6 inclusive.

3. Calculate [tex]$ f(x) $[/tex] for Each Possible [tex]$ x $[/tex]:
- For [tex]$ x = 0 $[/tex]: [tex]$ f(0) = 20(0) + 4 = 4 $[/tex]
- For [tex]$ x = 1 $[/tex]: [tex]$ f(1) = 20(1) + 4 = 24 $[/tex]
- For [tex]$ x = 2 $[/tex]: [tex]$ f(2) = 20(2) + 4 = 44 $[/tex]
- For [tex]$ x = 3 $[/tex]: [tex]$ f(3) = 20(3) + 4 = 64 $[/tex]
- For [tex]$ x = 4 $[/tex]: [tex]$ f(4) = 20(4) + 4 = 84 $[/tex]
- For [tex]$ x = 5 $[/tex]: [tex]$ f(5) = 20(5) + 4 = 104 $[/tex]
- For [tex]$ x = 6 $[/tex]: [tex]$ f(6) = 20(6) + 4 = 124 $[/tex]

4. List the Range Values:
- The range of the function, which is the set of possible total weights, is \{4, 24, 44, 64, 84, 104, 124\}.

Based on this analysis, the correct answer is option A: [tex]$\{4, 24, 44, 64, 84, 104, 124\}$[/tex].