Example: As shown in the figure, it shows the relationship between the daily sales revenue of Dongfeng Motorcycle Factory and the sales volume of motorcycles; And the relationship between the daily sales cost of motorcycle factory and motorcycle sales.
(1) Try to write the functional relationship between sales revenue and sales volume;
(2) Try to write the functional relationship between sales cost and sales volume;
(3) When the number of vehicles sold in a day is what, the sales revenue is equal to the sales cost?
(4) How many cars can the factory sell a day to make a profit?
Solution:? 1? y = x
2? Let y = kx+b
∵ Straight line? 0,2? 、? 4,4? At two o'clock,
∴ y=kx+2
Another 4=4k+2
∴k= 1/2
∴y= 1/2x+2
3? From the image, when x=4, sales revenue is equal to sales cost or x= 1/2x+2, ∴x=4.
4? From the image, when x>4 points, the factory can make a profit or x> 1/2x+2 is X >；; It won't be profitable until 4 o'clock.
Comments: Answer the questions according to the pictures. As long as you observe the image carefully, the answer is easy to find. The method of solving problems from functional images is "combination of numbers and shapes", that is, the corresponding seats (representation of numbers) are obtained from the corresponding points (features of shapes) on the images, and the shapes are represented by numbers, and the shapes reflect numbers, thus constructing the combination of numbers and shapes.
Second, change ideas.
Clever use of "transformation" is another feature of the thinking method in the study of "linear function": the problem of finding the function value is transformed into the problem of finding the algebraic value, the problem of finding the function relationship is transformed into the problem of column algebra, and the practical problem is transformed into the problem of function model, so as to solve the practical problem by using the concept and properties of the function.
: The length of candle lighting is in direct proportion to the lighting time. If a candle is lit for 6 minutes, the length of the remaining candle is12 cm; If it is 16 minutes, the remaining candle length is 7 cm; Suppose the candle is lit for x minutes, and the remaining candle is y cm long. Find the functional relationship between y and x, draw a picture, and find out how long this candle will burn out.
Train of thought analysis: the lighting length of the candle is proportional to the lighting time, so we can set a=kx(a is the lighting length), and if the candle length is b cm, then y=b-a, that is, y=b- kx, so the relationship between y and x is a linear function. Because the time of illumination is limited, its image is a line segment.
Solution: Let the candle be b cm long and burn kx cm (k>0) in x minutes, then y=b-kx.
According to the known conditions in the problem, when x=6, y =12; When x= 16, y=7.
It can be concluded that: 12=b-6k.
7= b- 16k
To solve this system of equations, k= 1/2.
b = 15
So the functional relationship between y and x is: y= 15- 1/2x.
X=30 when x=0, y= 15 and y=0.
Therefore, the line segment connecting two points A(0, 15) and B(30, 0) is the image of the function y= 15- 1/2 x(0≤x≤30), and the time for lighting the candle is 30 minutes.
Comments: The actual problem is transformed into a function model problem, so as to solve the actual problem by using the concept and nature of the function.
This article is the full text of the original. Users who don't have a PDF browser should download and install the original text first.