"Inverse Proportional Function" PPT courseware 7

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"Inverse Proportional Function" PPT courseware 7

Write the following functional relationship

1. When the distance s =10, the functional relationship between time t and speed v.

2. When the rectangular area S=5, the functional relationship between the length a and the width b.

3. When the triangle area S =20, the functional relationship between the base y and the height x of the triangle.

Please observe what common features these formulas have?

A function of the form y=k/x (k is a constant, k≠0) is called an inverse proportional function

Inverse proportional function y=k/x, then xy=k, k is a constant, and k≠0

Do it

1. Among the following functions, which ones are inversely proportional functions (x is the independent variable)?

(1) y=3/x (2) xy=-1/4 (3) x=-5y

2.y is the inverse proportional function of x. The following table gives some values ​​of x and y:

(1) Write the expression of this inverse proportional function;

(2) Complete the above table according to the function expression.

Solution: (1) Let y=k/x.

Substituting x= -1 and y=2 into the above formula, we get k= -2.

So y=-2/x.

think about it

If the graph of an inverse proportional function passes through the point (-2, 5), its analytical formula is y=-10/x.

If the intersection point of the graph of the linear function y=kx+b and the inverse proportional function y=k/x is (2, 3), then k=6, b=9.

It is known that point (2, 5) is on the image of the inverse proportional function y=□/x, where "□" is contaminated and unreadable writing, then the following points on the image of the inverse proportional function are ( )

A.(2,-5) B.(-5,-2)

C. (-3, 4) D. (4, -3)

summary:

(1) Content:

Inverse proportional function: meaning (expression) y=k/x (k≠0)

How to find the analytical expression xy=k (k≠0)

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Update Time: 2024-11-20

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