CN202939860U

CN202939860U - Inverse function demonstrator of exponential function

Info

Publication number: CN202939860U
Application number: CN 201220753078
Authority: CN
Inventors: 郭丽华; 张向平; 韦渤; 赵永建
Original assignee: Jinhua Polytechnic
Current assignee: Jinhua Polytechnic
Priority date: 2012-12-06
Filing date: 2012-12-06
Publication date: 2013-05-15
Anticipated expiration: 2022-12-06

Abstract

The utility model relates to a teaching appliance. An inverse function demonstrator of an exponential function mainly comprises a base, a slot frame, and glass plates. The slot frame is connected to an upper face of the base. The slot frame has a bottom slot and a side slot which are perpendicular to each other. The glass plates are rectangular. A plane rectangular coordinate system and a graph of the exponential function (y equals to ex) in the interval [-2, 2] are provided on the glass plates. The distance from the origin of the plane rectangular coordinate system to a left side edge of the glass plates is equal to the distance from the origin of the plane rectangular coordinate system to a bottom edge of the glass plates. The number of the glass plates is two. The inverse function demonstrator of the exponential function is reasonably designed, is simple in structure and low in cost, can vividly demonstrate the inverse function graph of the function, and can make students understand the graph position relation and the geometric significance of the function and the inverse function thereof in the same plane rectangular coordinate system.

Description

The inverse function demonstrator of exponential function

Technical field

The utility model relates to the inverse function demonstrator of education and instruction apparatus, particularly a kind of exponential function, can make the student when the inverse function of learning function, understands very intuitively the contrafunctional geometric meaning of exponential function between given area.

Background technology

The student has three steps while asking the inverse function of function y=f (x): first solve x=f (y); Again x is rewritten into to y, y is rewritten into to x; Finally using the codomain of function as contrafunctional field of definition, using the field of definition of function as contrafunctional codomain.When the student asks the inverse function of function in learning higher mathematics, if teaching aid demonstration intuitively can be arranged, have good effect, the inverse function demonstrator of described exponential function can address this problem, can demonstrate out the inverse function figure of function visually, and understand function graph position relation contrafunctional with it and geometric meaning in same plane right-angle coordinate.

The utility model content

In order to enrich the education and instruction apparatus, solve in higher mathematics and ask more contrafunctional apparent problem, the utility model provides a kind of inverse function demonstrator of exponential function, can demonstrate out the inverse function figure of function visually, and make the student understand function graph position relation contrafunctional with it and geometric meaning in same plane right-angle coordinate.

The scheme that the utility model adopts is:

The inverse function demonstrator of exponential function mainly consists of base, slot frame, glass plate, described slot frame is connected in above described base, described slot frame has orthogonal kerve and side channel, described glass plate is rectangle, has plane right-angle coordinate and exponential function y=e on described glass plate ^xFigure in interval [2,2], the initial point of described plane right-angle coordinate to the distance on limit, described glass plate left side with to described glass plate base apart from equating, described glass plate has identical two.We know, ask function y=e ^xInverse function the time, first obtain x=ln y; Be rewritten as again y=ln x; Finally, using the codomain of function as contrafunctional field of definition, using the field of definition of function as contrafunctional codomain, obtain function y=e ^xInverse function y=ln x.Said process is demonstrated with the inverse function demonstrator of described exponential function: first by a described glass plate from described slot frame is extracted out, plane is rotated counterclockwise 90 degree, then turns back to after the horizontal rotary turnback; Perhaps the plane dextrorotation turn 90 degrees, then turns back to after vertical rotary 180 degree, at this moment in same plane right-angle coordinate, has demonstrated function y=e ^xThe figure of inverse function y=ln x.

The beneficial effects of the utility model are:

The inverse function demonstrator of exponential function is reasonable in design, and the simple structure cost is low, can demonstrate out the inverse function figure of function visually, can make the student understand function graph position relation contrafunctional with it and geometric meaning in same plane right-angle coordinate.

The accompanying drawing explanation

Below in conjunction with figure of the present utility model, further illustrate:

Fig. 1 is the inverse function demonstrator schematic diagram of described exponential function;

Fig. 2 is the schematic diagram of described glass plate;

Fig. 3 is that the described glass plate plane of Fig. 2 is rotated counterclockwise 90 schematic diagram while spending;

Fig. 4 is the schematic diagram after the described glass plate horizontal rotary turnback of Fig. 3;

Fig. 5 is the schematic diagram after the described glass plate of Fig. 4 turns back to described slot frame again.

In figure, 1. base, 2. slot frame, 3. glass plate, 4. glass plate left side limit, 5. glass plate base.

Embodiment

As Fig. 1 be as described in the inverse function demonstrator schematic diagram of exponential function, mainly by base (1), slot frame (2), glass plate (3), formed, described slot frame (2) is connected in above described base (1), and described slot frame (2) has orthogonal kerve and side channel.

As Fig. 2 be as described in the schematic diagram of glass plate, described glass plate (3) is rectangle, has plane right-angle coordinate and exponential function y=e on described glass plate ^xFigure in interval [2,2], the initial point of described plane right-angle coordinate equates with the distance to described glass plate base (5) to the distance on described glass plate limit, left side (4).

As Fig. 3 be Fig. 2 as described in the glass plate plane be rotated counterclockwise 90 schematic diagram while spending, described glass plate (3) has identical two, Fig. 3 be by a described glass plate from described slot frame is extracted out, plane is rotated counterclockwise 90 schematic diagram while spending.

As Fig. 4 be Fig. 3 as described in schematic diagram after glass plate horizontal rotary turnback, be the rear view of Fig. 3.

As Fig. 5 be Fig. 4 as described in glass plate turn back to again as described in schematic diagram after the slot frame, demonstrated as seen function y=e in same plane right-angle coordinate ^xThe figure of inverse function y=ln x, function y=e ^xFigure and the figure of inverse function y=ln x about the y=x symmetry.

The teacher is to carry out about the y=x symmetry according to the figure of function figure contrafunctional with it when demonstration, step: first extract a described glass plate out plane from described slot frame and be rotated counterclockwise 90 degree, then turn back to after the horizontal rotary turnback; Perhaps the plane dextrorotation turn 90 degrees, then turns back to after vertical rotary 180 degree.Due to the initial point of described plane right-angle coordinate to the distance on described glass plate limit, left side (4) with to described glass plate base (5) apart from equating, after having guaranteed a described glass plate is turned back to, can make plane right-angle coordinate initial point and the coordinate axis of two described glass plates all overlap, drill visually and be illustrated in function and its inverse function figure in same plane right-angle coordinate, can make the student understand function graph position relation contrafunctional with it and geometric meaning in same plane right-angle coordinate.

Claims

1. the inverse function demonstrator of an exponential function, mainly by base, slot frame, glass plate, formed, it is characterized in that: described slot frame (2) is connected in above described base (1), described slot frame (2) has orthogonal kerve and side channel, described glass plate (3) is rectangle, has plane right-angle coordinate and exponential function y=e on described glass plate ^xFigure in interval [2,2], the initial point of described plane right-angle coordinate equates with the distance to described glass plate base (5) to the distance on described glass plate limit, left side (4).

2. the inverse function demonstrator of exponential function according to claim 1, it is characterized in that: described glass plate (3) has identical two.