Wyznacz wzór funkcji liniowej f , która spełnia warunki : a) f(-2)= - 4 i f(4)= - 1 b)f (-3)=2 i f(3)=6 c) f(-8)=6 i f(-3)=a d)f(0)=0 i f(√2) =2 

f(x) = ax + b y = ax + b a) f(-2) = -4  i  f(4) = -1 -4 = -2a + b -1 = 4a + b Odejmuję stronami: -4 - (-1) = -2a - 4a -4 + 1 = -6a -3 = -6a a = 1/2 -1 = 4 * 1/2 + b -1 = 2 + b b = -3 f(x) = 1/2x - 3 b) f(-3) = 2  i  f(3) = 6 2 = -3a + b 6 = 3a + b Odejmuję stronami: 2 - 6 = -3a - 3a -4 = -6a a = 2/3 6 = 3 * 2/3 + b 6 = 2 + b b = 4 f(x) = 2/3x + 4 c) f(-8) = 6  i  f(-3) = a 6 = -8a + b a = -3a + b Odejmuję stronami: 6 - a = -8a + 3a 6 - a = -5a 6 = -4a a = -3/2 6 = -8 * (-3/2) + b 6 = 12 + b b = -6 f(x) = -3/2x - 6 d) f(0) = 0  i  f(√2) = 2 0 = b 2 = √2a + b 2 = √2a a = 2/√2 = (2√2)/2 = √2 f(x) = √2 * x