Question

fie funtia f:R-R, f(x)=ax+5. Se stie ca punctul A(3;-1) apartine graficului functiei f. Determinati coordonatele punctelor de intersectie a graficului functiei f cu axele sistemului de axe ortogonale . Va rooooooooooogggggggggg multttttttttt

Answer 1

f(3)=-1
3a+5=-1
3a=-6
a=-2

f(x) =-2x+5

∩Oy...x=0 ...f(0)=5        ......................... B(0;5)
∩Ox...y=f(x)=0... -2x+5=0  x=5/2........A(5/2;0)

Answer 2

$f:\Bbb{R}\rightarrow \Bbb{R},\:\:f(x)=ax+5$
$A(3, -1)\in G_f\implies f(3)=-1$
$a\cdot 3+5=-1\implies a\cdot 3=-6\implies \boxed{a=-2}$
Prin urmare, $f(x)=-2x+5\:\:(\forall)\: x\in\Bbb{R}.$
$\text{Fie }\:G_f\:\cap\:Ox=\{A\}\implies y=0\implies -2x+5=0\\-2x=-5\implies x=\frac{5}{2}\implies\boxed{A(\frac{5}{2}, 0)}$
$\text{Fie }\:G_f\:\cap\:Oy=\{B\}\implies x=0\implies y=f(0)=5\implies \boxed{B(0, 5)}$

Intersectiile cu axele sunt punctele A(5/2, 0) si B(0, 5).