Answers to math questions about inverse proportional functions in the second grade of junior high school

A few simple math questions about inverse proportional functions for the second grade of junior high school

1. There are m identical machines working together, and it takes m hours to complete a task. Assume that x machines (X is a positive integer not greater than m) complete the same task, and the time required y (hours) and Functional expression of the total number of machines X;

The efficiency of a machine is: 1/(m*m)=1/m^2

y=1/(x*1/m^2)=m^2/x

2. Use images to solve inequalities: 2/x>x-1

y=2/x is the graph of the inverse proportional function, y=x-1 is the straight line, observing the graph shows that -1

It’s not easy to draw.

3. The graphs of the direct proportional function y=kx and the inverse proportional function y=k/x intersect at two points A and B. It is known that the abscissa of point A is 1 and the ordinate of point B is -4.

(1) Coordinates of two points A.B

(2) Write the relationship between these two functions

answer:

(1) The coordinates of A are (1,4)

The coordinates of B are (-1,-4)

Using the properties of direct proportional functions and inverse proportional functions,

Their two intersection points are symmetrical about the origin,

That is, the horizontal and vertical coordinates are opposite numbers to each other.

(2) Substitute the coordinates of points A and B into each analytical expression (substituting one is OK),

Get k=4

So y=4x

y=4/x

4. The annual electricity price of a certain ground is 0.8 yuan, and the annual electricity consumption is 100 million kilowatt-hours. This year, the electricity price is planned to be adjusted to between 0.55-0.75 yuan. After calculation, if the electricity price is adjusted by x yuan, the new electricity consumption this year will be Electricity y (100 million degrees) is inversely proportional to (x-0.4), and when x==0.65, y=0.8.

(1) Functional relationship between Y and X.

(2) If the cost of electricity per kilowatt hour is 0.3 yuan, at what yuan will the electricity price be adjusted to increase the revenue of the power department by 20% this year compared to the previous year? (Revenue = electricity consumption * (actual electricity price - cost)) Just list the equations and organize them.

(1)

y=k/(x-0.4)

0.8=k/(0.65-0.4)

k=0.2

So the functional formula is: y=0.2/(x-0.4), (0.55

(2) Last year’s income: 1*(0.8-0.3)=050 million yuan

(x-0.3)(y 1)=0.5*(1 20%)=0.6

(x-0.3)[0.2/(x-0.4) 1]=0.6

(x-0.3)(0.2 x-0.4)=0.6(x-0.4)

x^2-1.1x 0.3=0

(x-0.5)(x-0.6)=0

x=0.6

x=0.5 (discard if it does not meet the meaning of the question)

so:

When the electricity price is adjusted to 0.6 yuan, the income of the power department this year will increase by 20% compared with the previous year

Junior Grade 2 Inverse Proportional Function Question

1. It is known that the inverse proportional function y=k/x (k≠0) and the linear function y=-x-6.

(1) If the graphs of the linear function and the inverse proportional function intersect at point (-3, m), the values ​​of m and k;

(2) When k satisfies what conditions, these two function images have two different intersection points?

(3) When k=-2, assume that the intersection points of the two function images in (2) are A and B respectively. Try to determine which quadrant the two points A and B are in at this time? Is angle AOB acute or obtuse? (Just write the conclusion directly).

Answer: Solution:

⑴

The intersection point of ∵y=k/x and y=-x-6 is (-3,m),

∴Put x=-3 into the function y=-x-6,

y=-3, that is, m=-3.

∴The coordinates of the intersection point are (-3,-3).

Substituting (-3,-3) into the inverse/proportional function y=k/x, we get:

-3=k/-3 k=9

⑵

①∵The graph of a linear function passes through the second, third, and fourth quadrants,

∴whenk

② Connect y=-x-6 and y=k/x to form a system of equations, we get:

-x-6=k/x -x*x-6x=k x*x 6x k=0

When △x=b*b-4ac>0, the two images have two different intersection points.

△x=b*b-4ac=6*6-4*1*k>0

∴k

To sum up: when k

⑶Points A and B are in the second and fourth quadrants respectively, and the angle AOB is an obtuse angle.

Example 2. As shown in the figure, it is known that the graph of the linear function and the graph of the inverse proportional function intersect at two points A and B, and the abscissa of point A and the ordinate of point B are both: (1) linear Analytical expression of function;

(2)The area of ​​△AOB.

Analysis: This question is intended to examine the

relationship between the coordinates of the points on the function graph and the analytical formula of the function.

relationship and the method of the area of ​​geometric figures in the plane rectangular coordinate system, it should be noted that once

The key to the analytical expression of the function is to obtain the coordinates of the two points A and B, and the two points A and B are in the hyperbola

On the line, so their coordinates satisfy the analytical expression of the inverse proportional function; in question (2), knowing the coordinates of points A and B can know their distances to the x-axis and y-axis respectively.

Solution: (1) When x=-2, substitute y= – 8x to get y=4

When y=-2, x=4

∴The coordinates of point A are (-2, 4), and the coordinates of point B are (4,-2). Substitute them into

y=kx b, get:

Solutions have to:

∴The analytical formula of straight line AB is y=-x 2

(2) Suppose the straight line AB intersects the y-axis at point C, then the coordinates of point C are (0,2). ∴OC=2

S△AOB= S△AOC S△BOC=12 *2*∣-2∣ 12 *2*4=6

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