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 to the barbell, the total weight of the barbell and plates in pounds can be represented by [tex]f(x) = 20x + 4[/tex].

What is the range of the function for this situation?

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

To solve this problem, we first need to understand the context and requirements. We have a barbell that weighs 4 pounds by itself, and we can add up to 6 pairs of weight plates. Each pair of plates adds 20 pounds to the total weight.

The function representing this situation is:
[tex]\[ f(x) = 20x + 4 \][/tex]

Here, [tex]$ x $[/tex] represents the number of pairs of weight plates added to the barbell. Since there are up to 6 pairs, [tex]$ x $[/tex] can be any whole number from 0 to 6.

Steps to find the range of the function:

1. Identify the Domain:
The number of weight plate pairs, [tex]$ x $[/tex], can be {0, 1, 2, 3, 4, 5, 6}.

2. Calculate [tex]$ f(x) $[/tex] for each value in the domain:

- 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]

3. Compile the Results:
The possible values of [tex]$ f(x) $[/tex], which is the range of the function, are:
[tex]$\{4, 24, 44, 64, 84, 104, 124\}$[/tex]

So, the range of the function for this situation is:
[tex]\[ \{4, 24, 44, 64, 84, 104, 124\} \][/tex]

Looking at the provided options, the correct choice is B \{4, 24, 44, 64, 84, 104, 124\}.