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Answer :
To solve the problem of determining which statement is true regarding the function [tex]\( f(n) = 4n + 10 \)[/tex], we need to evaluate this function for specific values of [tex]\( n \)[/tex] mentioned in the options. Here's how we can do it step-by-step:
1. Understand the function:
The function given is [tex]\( f(n) = 4n + 10 \)[/tex]. This means for any integer value of [tex]\( n \)[/tex], you multiply it by 4 and then add 10 to get the value of the function.
2. Evaluate the function for the given options:
- Option A: [tex]\( f(-1) = 4(-1) + 10 = -4 + 10 = 6 \)[/tex]
- This matches the statement in option A, which states that [tex]\( f(-1) = 6 \)[/tex].
- Option B: [tex]\( f(0) = 4(0) + 10 = 0 + 10 = 10 \)[/tex]
- This value does not match the statement in option B, which claims [tex]\( f(0) = 40 \)[/tex].
- Option C: [tex]\( f(1) = 4(1) + 10 = 4 + 10 = 14 \)[/tex]
- This value does not match the statement in option C, which claims [tex]\( f(1) = 44 \)[/tex].
- Option D: [tex]\( f(10) = 4(10) + 10 = 40 + 10 = 50 \)[/tex]
- This matches the statement in option D, which states that [tex]\( f(10) = 50 \)[/tex].
3. Conclusion:
After evaluating the function for these specific values, we find that the true statements are Option A: [tex]\( f(-1) = 6 \)[/tex] and Option D: [tex]\( f(10) = 50 \)[/tex].
Therefore, both Options A and D are correct.
1. Understand the function:
The function given is [tex]\( f(n) = 4n + 10 \)[/tex]. This means for any integer value of [tex]\( n \)[/tex], you multiply it by 4 and then add 10 to get the value of the function.
2. Evaluate the function for the given options:
- Option A: [tex]\( f(-1) = 4(-1) + 10 = -4 + 10 = 6 \)[/tex]
- This matches the statement in option A, which states that [tex]\( f(-1) = 6 \)[/tex].
- Option B: [tex]\( f(0) = 4(0) + 10 = 0 + 10 = 10 \)[/tex]
- This value does not match the statement in option B, which claims [tex]\( f(0) = 40 \)[/tex].
- Option C: [tex]\( f(1) = 4(1) + 10 = 4 + 10 = 14 \)[/tex]
- This value does not match the statement in option C, which claims [tex]\( f(1) = 44 \)[/tex].
- Option D: [tex]\( f(10) = 4(10) + 10 = 40 + 10 = 50 \)[/tex]
- This matches the statement in option D, which states that [tex]\( f(10) = 50 \)[/tex].
3. Conclusion:
After evaluating the function for these specific values, we find that the true statements are Option A: [tex]\( f(-1) = 6 \)[/tex] and Option D: [tex]\( f(10) = 50 \)[/tex].
Therefore, both Options A and D are correct.
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