Get the most out of your questions with the extensive resources available on IDNLearn.com. Ask your questions and receive reliable, detailed answers from our dedicated community of experts.
Sagot :
To determine which function rule accurately models the given data in the table, let's test each function one by one by substituting the [tex]\( x \)[/tex] values and checking to see if we obtain the corresponding [tex]\( f(x) \)[/tex] values.
Given table:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -7 & -11 \\ \hline -1 & 1 \\ \hline 3 & 9 \\ \hline 4 & 11 \\ \hline 7 & 17 \\ \hline \end{array} \][/tex]
The function options are:
1. [tex]\( f(x) = 3x + 10 \)[/tex]
2. [tex]\( f(x) = 2x + 3 \)[/tex]
3. [tex]\( f(x) = 4x + 5 \)[/tex]
4. [tex]\( f(x) = 3x - 10 \)[/tex]
Let's test each function:
### Testing [tex]\( f(x) = 3x + 10 \)[/tex]:
- For [tex]\( x = -7 \)[/tex], [tex]\( f(-7) = 3(-7) + 10 = -21 + 10 = -11 \)[/tex]
- For [tex]\( x = -1 \)[/tex], [tex]\( f(-1) = 3(-1) + 10 = -3 + 10 = 7 \)[/tex] (does not match 1)
Since not all values match, this function is incorrect.
### Testing [tex]\( f(x) = 2x + 3 \)[/tex]:
- For [tex]\( x = -7 \)[/tex], [tex]\( f(-7) = 2(-7) + 3 = -14 + 3 = -11 \)[/tex]
- For [tex]\( x = -1 \)[/tex], [tex]\( f(-1) = 2(-1) + 3 = -2 + 3 = 1 \)[/tex]
- For [tex]\( x = 3 \)[/tex], [tex]\( f(3) = 2(3) + 3 = 6 + 3 = 9 \)[/tex]
- For [tex]\( x = 4 \)[/tex], [tex]\( f(4) = 2(4) + 3 = 8 + 3 = 11 \)[/tex]
- For [tex]\( x = 7 \)[/tex], [tex]\( f(7) = 2(7) + 3 = 14 + 3 = 17 \)[/tex]
All values match, so this function is correct.
### Checking the other functions for completeness:
#### Testing [tex]\( f(x) = 4x + 5 \)[/tex]:
- For [tex]\( x = -7 \)[/tex], [tex]\( f(-7) = 4(-7) + 5 = -28 + 5 = -23 \)[/tex] (does not match -11)
Since not all values match, this function is incorrect.
#### Testing [tex]\( f(x) = 3x - 10 \)[/tex]:
- For [tex]\( x = -7 \)[/tex], [tex]\( f(-7) = 3(-7) - 10 = -21 - 10 = -31 \)[/tex] (does not match -11)
Since not all values match, this function is incorrect.
Thus, the function rule that models the function over the given domain is:
[tex]\[ f(x) = 2x + 3 \][/tex]
Given table:
[tex]\[ \begin{array}{|c|c|} \hline x & f(x) \\ \hline -7 & -11 \\ \hline -1 & 1 \\ \hline 3 & 9 \\ \hline 4 & 11 \\ \hline 7 & 17 \\ \hline \end{array} \][/tex]
The function options are:
1. [tex]\( f(x) = 3x + 10 \)[/tex]
2. [tex]\( f(x) = 2x + 3 \)[/tex]
3. [tex]\( f(x) = 4x + 5 \)[/tex]
4. [tex]\( f(x) = 3x - 10 \)[/tex]
Let's test each function:
### Testing [tex]\( f(x) = 3x + 10 \)[/tex]:
- For [tex]\( x = -7 \)[/tex], [tex]\( f(-7) = 3(-7) + 10 = -21 + 10 = -11 \)[/tex]
- For [tex]\( x = -1 \)[/tex], [tex]\( f(-1) = 3(-1) + 10 = -3 + 10 = 7 \)[/tex] (does not match 1)
Since not all values match, this function is incorrect.
### Testing [tex]\( f(x) = 2x + 3 \)[/tex]:
- For [tex]\( x = -7 \)[/tex], [tex]\( f(-7) = 2(-7) + 3 = -14 + 3 = -11 \)[/tex]
- For [tex]\( x = -1 \)[/tex], [tex]\( f(-1) = 2(-1) + 3 = -2 + 3 = 1 \)[/tex]
- For [tex]\( x = 3 \)[/tex], [tex]\( f(3) = 2(3) + 3 = 6 + 3 = 9 \)[/tex]
- For [tex]\( x = 4 \)[/tex], [tex]\( f(4) = 2(4) + 3 = 8 + 3 = 11 \)[/tex]
- For [tex]\( x = 7 \)[/tex], [tex]\( f(7) = 2(7) + 3 = 14 + 3 = 17 \)[/tex]
All values match, so this function is correct.
### Checking the other functions for completeness:
#### Testing [tex]\( f(x) = 4x + 5 \)[/tex]:
- For [tex]\( x = -7 \)[/tex], [tex]\( f(-7) = 4(-7) + 5 = -28 + 5 = -23 \)[/tex] (does not match -11)
Since not all values match, this function is incorrect.
#### Testing [tex]\( f(x) = 3x - 10 \)[/tex]:
- For [tex]\( x = -7 \)[/tex], [tex]\( f(-7) = 3(-7) - 10 = -21 - 10 = -31 \)[/tex] (does not match -11)
Since not all values match, this function is incorrect.
Thus, the function rule that models the function over the given domain is:
[tex]\[ f(x) = 2x + 3 \][/tex]
Thank you for being part of this discussion. Keep exploring, asking questions, and sharing your insights with the community. Together, we can find the best solutions. IDNLearn.com is committed to your satisfaction. Thank you for visiting, and see you next time for more helpful answers.