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Authoritative PPT Summary
"First-time Function" PPT
Part One: Questions and Exploration
In 1996, ornithological researchers put a ring on a tern (migratory bird) in Finland; about 128 days later, people discovered it in Australia, 25,600 kilometers away.
(1) How many kilometers does this bird weighing more than 100 grams fly on average per day?
Solution: 25 600÷128 = 200 (km).
(2) What is the relationship between the tern’s journey y (unit: kilometers) and the flight time x (unit: days)?
Solution: y=200x (0≤x≤128).
(3) How many kilometers does this tern fly for one and a half months (a month is calculated as 30 days.)?
Solution: When x=45, y=200×45=9 000 (km)
Use your brain
What kind of function can be used to express the corresponding rules of variables in the following questions?
(1) The functional relationship between the perimeter C of the square and the side length x
C=4x
(2) The circumference L of the circle changes with the change of the radius r;
L=2πr
(3) The thickness of each exercise book is 0.5cm, and the total thickness h (unit cm) of some exercise books put together changes with the change of the number n of these exercise books;
h=0.5n
(4) Freeze a 0℃ object so that it drops by 2℃ every minute. The temperature T (unit: ℃) of the object changes with the freezing time t (unit: minutes).
T=-2t
First-order function PPT, the second part: induction and summary
Generally, a function of the form y=kx (k is a constant, k≠0) is called a proportional function, where k is called the proportional coefficient.
General form of proportional function
y = k x (constant for k≠0)
Note: Structural characteristics of proportional function y=kx (k≠0)
①k≠0
②The degree of x is 1
First-order function PPT, part 3: classroom exercises
Exercise 1. It is known that y-3 is directly proportional to x, and when x=4, y=7
Find: the functional relationship between y and x
Exercise 2. It is known that y is proportional to x-1, and when x=8, y=14
(1) Find the functional relationship between y and x
(2) Find the value of y when x=9.
Practice in class
1. The graph of the function y=-7x is in the __________ quadrant, passing through the points (0,___) and (1,___), and y increases with the increase of x.
2. In the image of the proportional function y=(k+1)x, y increases with the increase of x, then the value range of k is ______.
3. The image of the proportional function y=(m-1)x passes through the first and third quadrants, then the value range of m is ( )
A.m=1 B.m>1 C.m<1 D.m≥1
4. If the image of the proportional function y=(1-2m)x passes through points A(x1,y1) and B(x2,y2), when x1y2, then the value range of m is __________ .
5. The straight line y=(k2+3)x passes through the ________ quadrant, and y becomes ________ as x decreases.
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