If f is linear function such as that f(-1)= 2.5 and f(1)= -3, what is the value of f(4)?
A) 2.75
B) -8.25
C) -8.5
D) -11.25
E) -14
*I've been seeing this type of question a lot, while studying for SAT Math 2, but it seems that i can't get the hang of it. It would be great if someone explained the concept. Thanks:)
SAT Math 2 subject test question?
2020-08-08 10:35 pm
回答 (2)
2020-08-08 10:43 pm
✔ 最佳答案
Let f(x) = ax + b be the linear function.f(-1) = 2.5
a(-1) + b = 2.5
-a + b = 2,5 …… [1]
f(1) = -3
a(1) + b = -3
a + b = -3 …… [2]
[1] + [2]:
2b = -0.5
b = -0.25
[2] - [1]:
2a = -5.5
a = -2.75
Hence, f(x) = -2.75x - 0.25
f(4) = -2.75(4) - 0.25
f(4) = -11.25
The answer: D. -11.25
2020-08-08 11:30 pm
You are told that f is a linear function. Therefore put f(x) = ax + b.;
You are told f(-1) = 2.5 so 2.5 = a(-1) +b, ie., -a +b = 2.5...(1).;
You are told f(1) = -3 so -3 = a(1) +b, ie., a +b = -3.....(2).;
Now, add the 2 equations together and get 2b = 2.5 +(-3) = -0.5.;
Then b = -0.25 and (2) gives a = -b-3 = -(3+b) = -(3-0.25) = -2.75.;
Then f(x) = -2.75x -0.25 = -(2.75x+0.25).;
f(4) = -(4*2.75 +0.25) = -(11+0.25) = -11.25. Option D) gives correct answer.
You are told f(-1) = 2.5 so 2.5 = a(-1) +b, ie., -a +b = 2.5...(1).;
You are told f(1) = -3 so -3 = a(1) +b, ie., a +b = -3.....(2).;
Now, add the 2 equations together and get 2b = 2.5 +(-3) = -0.5.;
Then b = -0.25 and (2) gives a = -b-3 = -(3+b) = -(3-0.25) = -2.75.;
Then f(x) = -2.75x -0.25 = -(2.75x+0.25).;
f(4) = -(4*2.75 +0.25) = -(11+0.25) = -11.25. Option D) gives correct answer.
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