Problem:
Let f be a linear function with the properties that f(1)≤f(2),f(3)≥f(4), and f(5)=5. Which of the following statements is true?
Answer Choices:
A. f(0)<0
B. f(0)=0
C. f(1)<f(0)<f(−1)
D. f(0)=5
E. f(0)>5
Solution:
Since f is a linear function, it has the form f(x)=mx+b. Because f(1)≤f(2), we have m≥0. Similarly, f(3)≥f(4) implies m≤0. Hence, m=0, and f is a constant function. Thus, f(0)=f(5)=5.