Function, monotonicity and extrema
Answers are for parents and teachers.
1
If f(x) = 2x² − 3x + 1, find f(3).
10
2
If f(x) = x² − 4x, simplify f(a − 1).
(a − 1)² − 4(a − 1) = a² − 2a + 1 − 4a + 4 = a² − 6a + 5
3
The fuel in a car’s tank is B(s) = 45 − 0.08s litres (s — km driven). After how many km are 21 litres left?
300
4
A function is given on [−2, 4]: f(−2) = 7, f(1) = −2, f(4) = 10; it decreases on [−2, 1] and increases on [1, 4]. Find its greatest and least values.
Greatest 10, least −2.
5
Is “student → birth month” a function? What about “month → students born in it”? Explain.
The first is a function (each student has one birth month); the second usually is not, since several students may be born in one month.