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

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

Part One: Exploration

1. Are the points (x, y) corresponding to x and y that satisfy the relationship y= -2x+5 all on the graph of a linear function?

The points (x, y) corresponding to x and y that satisfy the relationship are all on the image.

2. Pick a few points on the image, find their abscissa and ordinate, and verify whether they satisfy the relationship y= -2x+5?

All points on the image satisfy the relationship.

Similarly, it has been mathematically proven that:

The graph of a linear function y= kx+b (b≠0) is a straight line.

Since two points determine a straight line, to draw the graph of a linear function, just trace the two points on the graph and then draw a straight line through the two points.

We often call this straight line "straight line y= kx+b".

PPT on the image and properties of a linear function, part 2: practice

1. Make a graph of y=2x?

2. Make an image of y=2x+1?

3. Make a graph of y= -2x+1?

analyze

From the above figure, we can see that for a linear function y=-2x+1, when the value of the independent variable x changes from small to large, the corresponding function value y changes from small to large.

From the above two examples, we can get:

A linear function y= kx+b (k≠0), when k>0, the function value increases with the increase of the independent variable; when k<0, the function value decreases with the increase of the independent variable.

For the specific derivation process, please refer to page 44 of the textbook. This derivation process is very important and every student must understand and master it.

The image and properties of a linear function PPT, the third part: summary

Summary: (for y=kx+b)

1. When k of two linear functions is the same but b is different, the graphs of the two functions are two straight lines parallel to each other, and they can be obtained by translation (up or down). The translation distance It's|b|.

2. When b of two linear functions is the same but k is different, the graphs of the two functions are two intersecting straight lines and intersect the y-axis at the same point, that is (0, b)

PPT on the image and properties of a linear function, part 4: extended questions

[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 rabbit 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.

[Example 3] A medical research institute developed a new drug. During the actual drug test, it was found that if adults take it at the prescribed dose, the drug content y (micrograms) per milliliter of blood changes with time x (hours) as follows: As shown in the picture, when an adult takes the prescribed dose of medicine.

(1) Find the functional relationship between y and x when 0≤ x ≤2 and x≥2;

Solution: (1) When 0≤ x ≤2, let y=kx(k≠0)

Since the image passes through the point (2,6), we substitute 6=2k, k=3

∴y=3x

When x ≥ 2, let y=kx+b(k≠0)

Because the image passes through point (2,6) and point (10,3),

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..

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

"Image and Properties of a linear function" PPT download Part 1: Learning objectives 1. Master the drawing method of the image 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 key points..

"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: 2024-10-03

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

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