Explain inverse proportionality

Explain inverse proportionality pmronionol. then functional &pendence between them is represented by the equation: where is a constant, A graph of an inverse proportionality is a curve. having two branches (Fig. _ I This curve is called a hyperbola. These curves are received at crossing a circular cone by a plane. As shown on Fig. l, a product of coordinates of a hyperbola points is a constant value. equal in this case to l. In general case this value is k. as it follows from a hyvvrbola equation: The main characteristics and properties of hyperbola: • tik• function domain: x O. and codomain: y 0; • the function is monotone (decreasing) at x O and at x > O. tut it is not monotone on the whole. because of a myint of discontinuity x = O • the function is untx»unded. discontinuous a IX»int x = O, odd. non-periodic; • there are no zeros of the function. A graph of parabola Of tt an origin of ordinate sys coefficient properties roots. All are shown The n

An inverse proportionality function is defined asf:fx=kxIf you write y=fx=kxxy=k is the equation of the curveThis is same as the equation of a rectangular hyperbolssee the given graphAs x0, y, so x=0 is not in its domainThe function is discontinuous at x=0. One can clearly see from the graph.It is a decreasing function as from the graph we can see as x increases fx decreasesfx is unbounded as x0, yfx0 for any x so it has no zeros

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