"Image and Properties of a linear function" PPT download

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"Image and Properties of a linear function" PPT download

Part One: Learning Objectives

1. Master how to draw the graph of a linear function and get a preliminary feel for its image.

2. Further understand the concepts and images of proportional functions and linear functions in the comparison of special and general functions

Key points: the image of a linear function

Difficulty: The exploration process of combining the graph and properties of a linear function with the expression y=kx+b

Review and Reflection

1. What is a linear function?

2. What are the images and properties of proportional functions?

3. What is the relationship between proportional functions and linear functions?

The image and properties of a linear function PPT, the second part: creation problem

Since the proportional function is a special linear function and the graph of the proportional function is a straight line, then the graph of the linear function will also be a straight line. What is the relationship between their images? What are the properties of a linear function?

1. Please draw the graphs of the following functions y=x, y=x+2, y=x-2 in the same coordinate system.

2. Observe and compare

Discuss: What are the similarities and differences between the graphs of the proportional function y=x and the linear functions y=x+2 and y=x-2.

Summary: The shapes of the graphs of these two functions are _____, and the graph of the tilt function y=x passes through the origin, and the graph of the function y=x+2 intersects the y-axis at the point _____, that is, it can be seen It is obtained by translating the straight line y=x to _____ by _____ unit length. The graph of the function y=x-2 intersects the y-axis at the point _____, that is, it can be seen as being translated from the straight line y=x to _____ by _____ unit lengths.

3. Explore

(1) Compare the analytical expressions and images of their functions. Can you explain why this is?

(2) Can you tell what shape the graph of the linear function y=3x-4 is? How does it relate to the straight line y=3x?

(3) So what is the relationship between the image of the linear function y=kx+b and the image of the proportional function y=kx?

The graph of the linear function y=kx+b is a straight line. We call it the straight line y=kx+b. It can be seen as the straight line y=kx translated by b units of length.

PPT on the image and properties of a linear function, part 3: Consolidation exercises:

1. Among the following functions, the function whose value of y increases as the value of x increases is ________.

A.y=-2x B.y=-2x+1

C.y=x-2 D.y=-x-2

2. The straight line y=3x-2 can be obtained by translating the straight line y=3x to _____ by _____ units.

3. The straight line y=x+2 can be obtained by translating the straight line y=x-1 to _____ by _____ units.

PPT on the image and properties of a linear function, part 4: knowledge expansion

[Example 1] Known: function y = (m+1) x + 2 m�6

(1) If the graph of the function passes (-1, 2), find the analytical formula of this function.

(2) If the function graph is parallel to the straight line y = 2 x + 5, find the analytical formula of its function.

(3) Find the intersection point of the straight line that satisfies the condition (2) and the straight line y = �3 x + 1, and

Find the area of ​​the triangle enclosed by these two straight lines and the y-axis.

[Example 2] The following figures l1 and l2 are respectively the function graphs between distance and time in the tortoise and the hare race.

You can know from the image:

(1) This time it is a ____ meter race.

(2) The image representing the rabbit is ____.

(3) When the rabbit reaches the end point, the tortoise is still ___ meters away from the end point.

(4) If the tortoise and the hare reach the finish line at the same time, the tortoise must run ___ meters first.

(5) The tortoise must reach the finish line first, at least ___ minutes earlier than the hare.

PPT on the image and properties of a linear function, Part 5: Class summary

1. Be able to draw the graph of a function

2. The image and properties of a linear function, the meaning and role of the constants k and b.

3. Ideas and methods of combining numbers and shapes, from special to general ideas and methods

4. Further experience the general ideas and methods of studying functions

Keywords: Free download of Hebei Education Edition mathematics PPT courseware for eighth grade volume 2, PPT download of images and properties of linear functions, .PPT format;

For more information about the "Image and Properties of a linear function" PPT courseware, please click the "Image and Properties of a linear function ppt" tag.

Download the PPT courseware of "The Image and Properties of a Linear Function":

"The Image and Properties of a Linear Function" PPT courseware download part one content: The image of a function takes the values ​​of the independent variable x and the corresponding dependent variable y of a function as the abscissa and ordinate of the point respectively, and depicts them in the rectangular coordinate system Its corresponding points, all these point groups..

"The Image and Properties of a Linear Function" PPT courseware:

"The Image and Properties of a linear function" PPT courseware Part 1: Exploration 1. Are the points (x, y) corresponding to x and y that satisfy the relationship y= -2x+5 all on the image of a linear function? The points (x, y) corresponding to x and y that satisfy the relationship are all on the image. 2..

"The Image and Properties of a Linear Function" PPT:

"The Image and Properties of a Linear Function" PPT Part One Content: Learning Objectives: 1. Experience the drawing process and initially understand the general steps of making a function image; 2. Understand the correspondence between the algebraic expression and the image of a linear function; 3 .Be able to write a letter more skillfully..

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Update Time: 2024-07-06

This template belongs to Mathematics courseware Hebei Education Edition Eighth Grade Mathematics Volume 2 industry PPT template

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