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Answer :
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\}.
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\}.
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