Find expert answers and community-driven knowledge on IDNLearn.com. Our platform offers detailed and accurate responses from experts, helping you navigate any topic with confidence.
Sagot :
To determine which function was used to generate the given values of [tex]\( f(x) \)[/tex], we need to evaluate each option for the provided [tex]\( x \)[/tex] values and see which function produces the sequence [tex]\( \{6, 9, 14, 21\} \)[/tex].
Let's evaluate each given function step-by-step:
### Option A: [tex]\( f(x) = 2x + 4 \)[/tex]
1. For [tex]\( x = 1 \)[/tex]:
[tex]\( f(1) = 2(1) + 4 = 2 + 4 = 6 \)[/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\( f(2) = 2(2) + 4 = 4 + 4 = 8 \)[/tex]
3. For [tex]\( x = 3 \)[/tex]:
[tex]\( f(3) = 2(3) + 4 = 6 + 4 = 10 \)[/tex]
4. For [tex]\( x = 4 \)[/tex]:
[tex]\( f(4) = 2(4) + 4 = 8 + 4 = 12 \)[/tex]
The values are [tex]\( \{6, 8, 10, 12\} \)[/tex], which does not match the given sequence.
### Option B: [tex]\( f(x) = x^2 + 5 \)[/tex]
1. For [tex]\( x = 1 \)[/tex]:
[tex]\( f(1) = 1^2 + 5 = 1 + 5 = 6 \)[/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\( f(2) = 2^2 + 5 = 4 + 5 = 9 \)[/tex]
3. For [tex]\( x = 3 \)[/tex]:
[tex]\( f(3) = 3^2 + 5 = 9 + 5 = 14 \)[/tex]
4. For [tex]\( x = 4 \)[/tex]:
[tex]\( f(4) = 4^2 + 5 = 16 + 5 = 21 \)[/tex]
The values are [tex]\( \{6, 9, 14, 21\} \)[/tex], which matches the given sequence.
### Option C: [tex]\( f(x) = x + 5 \)[/tex]
1. For [tex]\( x = 1 \)[/tex]:
[tex]\( f(1) = 1 + 5 = 6 \)[/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\( f(2) = 2 + 5 = 7 \)[/tex]
3. For [tex]\( x = 3 \)[/tex]:
[tex]\( f(3) = 3 + 5 = 8 \)[/tex]
4. For [tex]\( x = 4 \)[/tex]:
[tex]\( f(4) = 4 + 5 = 9 \)[/tex]
The values are [tex]\( \{6, 7, 8, 9\} \)[/tex], which does not match the given sequence.
### Option D: [tex]\( f(x) = 2x^2 + 4 \)[/tex]
1. For [tex]\( x = 1 \)[/tex]:
[tex]\( f(1) = 2(1)^2 + 4 = 2 + 4 = 6 \)[/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\( f(2) = 2(2)^2 + 4 = 8 + 4 = 12 \)[/tex]
3. For [tex]\( x = 3 \)[/tex]:
[tex]\( f(3) = 2(3)^2 + 4 = 18 + 4 = 22 \)[/tex]
4. For [tex]\( x = 4 \)[/tex]:
[tex]\( f(4) = 2(4)^2 + 4 = 32 + 4 = 36 \)[/tex]
The values are [tex]\( \{6, 12, 22, 36\} \)[/tex], which does not match the given sequence.
Upon evaluating all options, we see that only Option B ([tex]\( f(x) = x^2 + 5 \)[/tex]) matches the given sequence [tex]\( \{6, 9, 14, 21\} \)[/tex].
Therefore, the function used to make the pattern is:
[tex]\[ \boxed{f(x) = x^2 + 5} \][/tex]
Let's evaluate each given function step-by-step:
### Option A: [tex]\( f(x) = 2x + 4 \)[/tex]
1. For [tex]\( x = 1 \)[/tex]:
[tex]\( f(1) = 2(1) + 4 = 2 + 4 = 6 \)[/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\( f(2) = 2(2) + 4 = 4 + 4 = 8 \)[/tex]
3. For [tex]\( x = 3 \)[/tex]:
[tex]\( f(3) = 2(3) + 4 = 6 + 4 = 10 \)[/tex]
4. For [tex]\( x = 4 \)[/tex]:
[tex]\( f(4) = 2(4) + 4 = 8 + 4 = 12 \)[/tex]
The values are [tex]\( \{6, 8, 10, 12\} \)[/tex], which does not match the given sequence.
### Option B: [tex]\( f(x) = x^2 + 5 \)[/tex]
1. For [tex]\( x = 1 \)[/tex]:
[tex]\( f(1) = 1^2 + 5 = 1 + 5 = 6 \)[/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\( f(2) = 2^2 + 5 = 4 + 5 = 9 \)[/tex]
3. For [tex]\( x = 3 \)[/tex]:
[tex]\( f(3) = 3^2 + 5 = 9 + 5 = 14 \)[/tex]
4. For [tex]\( x = 4 \)[/tex]:
[tex]\( f(4) = 4^2 + 5 = 16 + 5 = 21 \)[/tex]
The values are [tex]\( \{6, 9, 14, 21\} \)[/tex], which matches the given sequence.
### Option C: [tex]\( f(x) = x + 5 \)[/tex]
1. For [tex]\( x = 1 \)[/tex]:
[tex]\( f(1) = 1 + 5 = 6 \)[/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\( f(2) = 2 + 5 = 7 \)[/tex]
3. For [tex]\( x = 3 \)[/tex]:
[tex]\( f(3) = 3 + 5 = 8 \)[/tex]
4. For [tex]\( x = 4 \)[/tex]:
[tex]\( f(4) = 4 + 5 = 9 \)[/tex]
The values are [tex]\( \{6, 7, 8, 9\} \)[/tex], which does not match the given sequence.
### Option D: [tex]\( f(x) = 2x^2 + 4 \)[/tex]
1. For [tex]\( x = 1 \)[/tex]:
[tex]\( f(1) = 2(1)^2 + 4 = 2 + 4 = 6 \)[/tex]
2. For [tex]\( x = 2 \)[/tex]:
[tex]\( f(2) = 2(2)^2 + 4 = 8 + 4 = 12 \)[/tex]
3. For [tex]\( x = 3 \)[/tex]:
[tex]\( f(3) = 2(3)^2 + 4 = 18 + 4 = 22 \)[/tex]
4. For [tex]\( x = 4 \)[/tex]:
[tex]\( f(4) = 2(4)^2 + 4 = 32 + 4 = 36 \)[/tex]
The values are [tex]\( \{6, 12, 22, 36\} \)[/tex], which does not match the given sequence.
Upon evaluating all options, we see that only Option B ([tex]\( f(x) = x^2 + 5 \)[/tex]) matches the given sequence [tex]\( \{6, 9, 14, 21\} \)[/tex].
Therefore, the function used to make the pattern is:
[tex]\[ \boxed{f(x) = x^2 + 5} \][/tex]
Thank you for using this platform to share and learn. Don't hesitate to keep asking and answering. We value every contribution you make. Find clear answers at IDNLearn.com. Thanks for stopping by, and come back for more reliable solutions.