Properties of 15.6 linear function (1)

First, the teaching objectives

1, so that students can master the related properties of a function and use the properties to solve simple problems.

2. Through the process of drawing, observing and discovering, cultivate students' ability of observing and summarizing, and infiltrate the mathematical thinking method of combining numbers and shapes into students.

3. Cultivate students' good habits and sense of cooperation through the process of drawing, observing and discovering.

Second, the teaching focus: let students master the nature and simple application of a function.

Third, teaching difficulties: understanding the influence of K and B in y=kx+b(k≠0) on images.

Fourth, teaching methods:

Observation and analysis of the combination of teaching and practice

Five, teaching tools: multimedia

Sixth, the teaching process.

First, create a situation

In order to welcome the 2008 Olympic Games, Metro Line 5 was officially put into operation this year1October 7th, 65438. Like a dragon, it bridges the north and south of Beijing and relieves the traffic pressure in Beijing. The total length of Metro Line 5 (Tiantongyuan to Songjiazhuang) is about 28 kilometers, with an average running speed of about 40 kilometers per hour.

Question 1: The functional relationship between the distance S (km) from Songjiazhuang after the subway line 5 leaves Tiantongyuan and the travel time t (hours) is as follows.

Question 2: How does the distance s (kilometers) from Songjiazhuang change and decrease with the increase of driving time t (hours)? What determines that s decreases with the increase of t?

Next, on the basis of learning function mirroring once,

Let's continue to discuss: the essence of linear function!

Second, explore new knowledge.

1. Study the following four groups of linear functions.

( 1) y=-2x+3，y=-2x，y=-2x-2 .

(2)y= - 2x+2 y= -x+2 y=- +2

(3)y= +2 y= y= -3

(4)y= 2x-3，y= x-3，y= -3 .

Inquiry content: the properties of linear function y=kx+b(k 0)

The Influence of 1.b on Function Images

The query conclusion 1:B has the same value and the image intersection is the same (0, b).

Inquiry conclusion 2: The symbol of B determines the position of the intersection between the image and the Y axis.

The b>0 image crosses the positive semi-axis of the Y axis.

B=0 The image intersects the Y axis at the origin.

The b & lt0° image intersects the Y axis at the negative semi-axis.

2. The influence of K on function images

The images with the same query conclusion 1:K are parallel to each other.

Inquiry conclusion 2: the symbol of k determines the changing trend of linear function image y with X.

K>0 low left and high right,

In the first and third quadrants, y increases with the increase of x.

K<0 is high left and low right.

Y decreases with the increase of X in the second and fourth quadrants.

3. Explore the conclusion:

Analytical formula: y=kx+b(k 0)

Image y

0 x

y

0 x

y

0 x

y

0 x

y

0 x

y

0 x

k

b

Third, summary:

Important properties of linear function y=kx+b(k≠ 0);

K>0, Y increases with the increase of X, and the graph must have one or three quadrants.

K<0, Y decreases with the increase of X, and the graph must pass through two or four quadrants.

Fourth, consolidate new knowledge.

1, case study:

The function y=(2m+6)x-m is a linear function about x.

① If the image intersects the Y axis on the positive semi-axis of the Y axis, what is the range of m?

If y decreases with the increase of x, please indicate which quadrants the image passes through.

(* * * explained)

2 exercises on the properties of a function:

(1) when k >: 0, y increases with x,

(2) When k < 0, y increases with X. 。

(3) The symbolic relationship between the image of linear function and K and B;

(Draw a sketch)

The function of k is to determine the changing trend of linear function image y with X.

Function of B: The symbol of B determines the position of the intersection of the image and the Y axis.

(4) Small exercises

1. If y increases with the increase of x, the image of the proportional function y=kx passes ().

(a) The first and second quadrants and the origin

(b) The first three quadrants and the origin

(c) The second and third quadrants and the origin

(d) the second quadrant and the origin

2. The straight line parallel to the straight line y=5x+7 is ().

(A)y=5x (C)y=

y=-5x+7 (D)y=

3. The image of the linear function y=kx+b is shown in the figure, so the condition that k and b meet is ().

(A)k & gt； 0，b & gt0(B)k & gt； 0，b & lt0

(C)k & lt； 0，b & gt0 (D) k<0，b & lt0

V. Summary of cooperation between teachers and students:

Properties of linear functions:

Image properties of y=kx+b

Increase or decrease through the quadrant of a straight line

k & gt0b & gt； 0

The first, second and third quadrants y increase with the increase of x.

b=0

Y in the first and third quadrants increases with the increase of x.

b & lt0

Y in the first, third and fourth quadrants increases with the increase of X.

Image properties of y=kx+b

Increase or decrease through the quadrant of a straight line

K & lt0b & gt； 0

Y in the first, second and fourth quadrants decreases with the increase of x.

b=0

Y in the second and fourth quadrants decreases with the increase of x.

b & lt0

Y in the second, third and fourth quadrants decreases with the increase of x.

Seven. Assignment 1, textbook P3 1, exercises 3, 4 P32, 6.7.

2. Thinking question: P33, a textbook in C.

blackboard-writing design

Subject:-

Explore 1-

Survey 2- Practice.

To sum up the rules:-.

Reflection after class:

For reference: the first network of the new curriculum standard,

Serve you education network

Excellent courseware of middle school teachers' network