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Answer :
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].
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].
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