"First-time Function" PPT

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"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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Update Time: 2024-10-19

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