The Vertical Line That Touches Once
Difficulty: Medium · Topics: Algebra, Functions, Function Values
Bir marta tegadigan vertikal chiziq
The curve x=y^2-2y is drawn below. It is not the graph of a function y=f(x), because most vertical lines meet it twice.
graph "x":[-2,5],"y":[-2.4,4],"xTicks":[-2,-1,1,2,3,4,5],"yTicks":[-2,-1,1,2,3,4],"grid":true,"clip":true,"label":"Sideways parabola x = y squared minus 2y","items":["type":"curve","points":[[4.76,-1.4],[4.29,-1.3],[3.84,-1.2],[3.41,-1.1],[3,-1],[2.61,-0.9],[2.24,-0.8],[1.89,-0.7],[1.56,-0.6],[1.25,-0.5],[0.96,-0.4],[0.69,-0.3],[0.44,-0.2],[0.21,-0.1],[0,0],[-0.19,0.1],[-0.36,0.2],[-0.51,0.3],[-0.64,0.4],[-0.75,0.5],[-0.84,0.6],[-0.91,0.7],[-0.96,0.8],[-0.99,0.9],[-1,1],[-0.99,1.1],[-0.96,1.2],[-0.91,1.3],[-0.84,1.4],[-0.75,1.5],[-0.64,1.6],[-0.51,1.7],[-0.36,1.8],[-0.19,1.9],[0,2],[0.21,2.1],[0.44,2.2],[0.69,2.3],[0.96,2.4],[1.25,2.5],[1.56,2.6],[1.89,2.7],[2.24,2.8],[2.61,2.9],[3,3],[3.41,3.1],[3.84,3.2],[4.29,3.3],[4.76,3.4]],"start":"arrow","end":"arrow","type":"line","from":[-1,-2.3],"to":[-1,3.9],"dash":true,"ink":true,"width":1.1,"type":"point","at":[-1,1],"label":"(−1, 1)","anchor":"w","italic":false]
The vertical line x=k meets the curve at exactly one point. Find k.
Quyida x=y^2-2y egri chiziq chizilgan. U y=f(x) funksiyaning grafigi emas , chunki ko‘pchilik vertikal chiziqlar uni ikki marta kesadi.
graph "x":[-2,5],"y":[-2.4,4],"xTicks":[-2,-1,1,2,3,4,5],"yTicks":[-2,-1,1,2,3,4],"grid":true,"clip":true,"label":"Sideways parabola x = y squared minus 2y","items":["type":"curve","points":[[4.76,-1.4],[4.29,-1.3],[3.84,-1.2],[3.41,-1.1],[3,-1],[2.61,-0.9],[2.24,-0.8],[1.89,-0.7],[1.56,-0.6],[1.25,-0.5],[0.96,-0.4],[0.69,-0.3],[0.44,-0.2],[0.21,-0.1],[0,0],[-0.19,0.1],[-0.36,0.2],[-0.51,0.3],[-0.64,0.4],[-0.75,0.5],[-0.84,0.6],[-0.91,0.7],[-0.96,0.8],[-0.99,0.9],[-1,1],[-0.99,1.1],[-0.96,1.2],[-0.91,1.3],[-0.84,1.4],[-0.75,1.5],[-0.64,1.6],[-0.51,1.7],[-0.36,1.8],[-0.19,1.9],[0,2],[0.21,2.1],[0.44,2.2],[0.69,2.3],[0.96,2.4],[1.25,2.5],[1.56,2.6],[1.89,2.7],[2.24,2.8],[2.61,2.9],[3,3],[3.41,3.1],[3.84,3.2],[4.29,3.3],[4.76,3.4]],"start":"arrow","end":"arrow","type":"line","from":[-1,-2.3],"to":[-1,3.9],"dash":true,"ink":true,"width":1.1,"type":"point","at":[-1,1],"label":"(−1, 1)","anchor":"w","italic":false]
x=k vertikal chiziq egri chiziq bilan aynan bitta nuqtada kesishadi. k ni toping.