Final answer:
The correct function that matches the given values f(2)=4 and f(-1)=-5 is option d, which is f(x) = 3x - 2.
Step-by-step explanation:
The student is looking for a function f(x) that satisfies the conditions f(2)=4 and f(-1)=-5. To solve this, substitute the given x-values into each function option and check if the resulting y-values match the conditions given.
- Option a: f(x) = 3x - 11
- Option b: f(x) = (1/3)x - 2
- Option c: f(x) = 3x - 10
- Option d: f(x) = 3x - 2
- Option e: f(x) = -3x - 2
By substituting x = 2 and x = -1 into each option,
- For option a: f(2) = 3(2) - 11 = -5 (Does not match)
- For option b: f(2) = (1/3)(2) - 2 = -4/3 (Does not match)
- For option c: f(2) = 3(2) - 10 = -4 (Does not match)
- For option d: f(2) = 3(2) - 2 = 4 and f(-1) = 3(-1) - 2 = -5 (Matches both conditions)
- For option e: f(2) = -3(2) - 2 = -8 (Does not match)
Therefore, the correct answer is option d: f(x) = 3x - 2.