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 .
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Answer 1

[tex]A(x_A,y_A)\in Gf\Leftrightarrow f(x_a)=y_A\\ f(x)=ax+5\\ A(3, -1)\in Gf\Leftrightarrow a\cdot 3+5=-1\Leftrightarrow 3a=-6\Leftrightarrow a=-2\\ f(x)=-2x+5\\ Intersec\c tia\, cu\, Ox:\\ Gf\cap Ox: y=0\Leftrightarrow f(x)=0\Leftrightarrow -2x+5=0 \Leftrightarrow -2x=-5\Leftrightarrow x=\frac{5}{2}\\ \Rightarrow B(\frac{5}{2}, 0)\\ Intersec\c tia\, cu\, Oy:\\ Gf\cap Oy: x=0\Leftrightarrow f(x)=-2\cdot 0+5=5\Rightarrow C(0, 5)\\ Gf\cap Ox=\{B(\frac{5}{2}, 0)\}\\ Gf\cap Oy=\{C(0, 5)\}[/tex]