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Answer :
To solve the problem of finding 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, and each pair of plates weighs 20 lb, we need to calculate the total weight for different values of [tex]\(x\)[/tex].
### Step-by-Step Solution:
1. Identify the possible values for [tex]\(x\)[/tex]:
The question specifies that there can be up to 6 pairs of weight plates. Therefore, the possible values for [tex]\(x\)[/tex] are 0, 1, 2, 3, 4, 5, and 6.
2. Substitute each value of [tex]\(x\)[/tex] into the function [tex]\(f(x) = 20x + 4\)[/tex]:
- For [tex]\(x = 0\)[/tex]: [tex]\(f(0) = 20 \times 0 + 4 = 4\)[/tex]
- For [tex]\(x = 1\)[/tex]: [tex]\(f(1) = 20 \times 1 + 4 = 24\)[/tex]
- For [tex]\(x = 2\)[/tex]: [tex]\(f(2) = 20 \times 2 + 4 = 44\)[/tex]
- For [tex]\(x = 3\)[/tex]: [tex]\(f(3) = 20 \times 3 + 4 = 64\)[/tex]
- For [tex]\(x = 4\)[/tex]: [tex]\(f(4) = 20 \times 4 + 4 = 84\)[/tex]
- For [tex]\(x = 5\)[/tex]: [tex]\(f(5) = 20 \times 5 + 4 = 104\)[/tex]
- For [tex]\(x = 6\)[/tex]: [tex]\(f(6) = 20 \times 6 + 4 = 124\)[/tex]
3. List the weights obtained from each calculation:
The weights calculated for each possible [tex]\(x\)[/tex] are 4, 24, 44, 64, 84, 104, and 124.
4. Identify the range:
The range of the function given the possible values of [tex]\(x\)[/tex] is the set of weights calculated: [tex]\(\{4, 24, 44, 64, 84, 104, 124\}\)[/tex].
Therefore, the correct choice for the range of the function is B [tex]\(\{4, 24, 44, 64, 84, 104, 124\}\)[/tex].
### Step-by-Step Solution:
1. Identify the possible values for [tex]\(x\)[/tex]:
The question specifies that there can be up to 6 pairs of weight plates. Therefore, the possible values for [tex]\(x\)[/tex] are 0, 1, 2, 3, 4, 5, and 6.
2. Substitute each value of [tex]\(x\)[/tex] into the function [tex]\(f(x) = 20x + 4\)[/tex]:
- For [tex]\(x = 0\)[/tex]: [tex]\(f(0) = 20 \times 0 + 4 = 4\)[/tex]
- For [tex]\(x = 1\)[/tex]: [tex]\(f(1) = 20 \times 1 + 4 = 24\)[/tex]
- For [tex]\(x = 2\)[/tex]: [tex]\(f(2) = 20 \times 2 + 4 = 44\)[/tex]
- For [tex]\(x = 3\)[/tex]: [tex]\(f(3) = 20 \times 3 + 4 = 64\)[/tex]
- For [tex]\(x = 4\)[/tex]: [tex]\(f(4) = 20 \times 4 + 4 = 84\)[/tex]
- For [tex]\(x = 5\)[/tex]: [tex]\(f(5) = 20 \times 5 + 4 = 104\)[/tex]
- For [tex]\(x = 6\)[/tex]: [tex]\(f(6) = 20 \times 6 + 4 = 124\)[/tex]
3. List the weights obtained from each calculation:
The weights calculated for each possible [tex]\(x\)[/tex] are 4, 24, 44, 64, 84, 104, and 124.
4. Identify the range:
The range of the function given the possible values of [tex]\(x\)[/tex] is the set of weights calculated: [tex]\(\{4, 24, 44, 64, 84, 104, 124\}\)[/tex].
Therefore, the correct choice for the range of the function is B [tex]\(\{4, 24, 44, 64, 84, 104, 124\}\)[/tex].
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