Daca graficul functiei trece prin punctele A(2;7) si B(-1;-2), inseamna ca:
[tex] \left \{ {{f(2)=7} \atop {f(-1)=-2}} \right. [/tex]
f(2)=2a+b
f(-1)=-a+b
Si avem sistemul:
[tex] \left \{ {{2a+b=7} \atop {-a+b=-2}} \right. [/tex]
Daca scadem cele doua relatii avem:
2a-(-a)+b-b=7-(-2)
2a+a=7+2
3a=9
a=3
[tex] \left \{ {{a=3} \atop {-a+b=-2}} \right. [/tex]
[tex] \left \{ {{a=3} \atop {-3+b=-2}} \right. [/tex]
[tex] \left \{ {{a=3} \atop {b=1}} \right. [/tex]
Finalizare:
f: R->R, f(x)=3x+1
