Features
Features:

Product Tour >

Edraw AI >

Paid Plans:

Individuals >

Business >

Eduaction >
Resources
Blog

History

How-tos & Tips

Discovery

Biography

Business Analysis

Examples

AI concept Map

Free AI Mind Map Generator

Onenote Mind Map

Bcg Matrix Examples

Nike Marketing Strategy

Unilever SWOT Analysis

Make Mind Maps in Google Docs

Guide

FAQs

What's New

Resource Center
Templates
All Templates

Brain Storming Templates

Strategy and Planning Templates

Project Management Templates

Product Management Templates

Human Resources Templates

Agile Workflow Templates

Marketing Templates

Education Templates

Fun and Games Templates

User Gallery
Download
Pricing
Enterprise

proportional function

This is a mind map about proportional functions. The main content includes: practice consolidation and classic examples. Used for review and preview to improve learning efficiency.

Edited at 2024-04-10 20:46:36

PlotWizard

Recent works View more works>>

proportional function

PlotWizard

Recent works View more works>>

Recommended to you
Outline

Trigonometric functions
- 430
- 1
PlotWizard
Lines and angles
- 67
PlotWizard
quadratic radical
- 68
PlotWizard
special parallelogram
- 26
Mason·Carter
The concept of trigonometric functions
- 9
MM
round
- 22
Mason·Carter
The concept and properties of functions
- 26
Mason·Carter
Parallel and intersection lines (1)
- 40
Mason·Carter
Equations (Systems) and their applications
- 17
EllaGrace
One-element equation
- 22
EllaGrace

proportional function

1. Classic examples

1. Definition of proportional function

[Answer and analysis]

【Answer】

2. Image and properties of proportional function

[Ideas] Find two points on each function graph, draw the graph, and answer the question based on the characteristics of the function graph. [Answer and analysis] Solution: List: Draw points and connect lines: [Summary and sublimation] This question examines the use of point drawing method to draw the image of a function. The specific steps are listing, drawing points, and connecting lines.

Then the function value y increases with the value of the independent variable x. (Fill in "increase" or "decrease")

【Idea Tip】Judge based on the properties of the proportional function. 【Answer】Decrease; [Analysis] Solution: Substituting the point (-6, 2) into y=kx, we get: 2=-6k, Then the function value y decreases as the value of the independent variable x increases.

[Variation] Among the following statements about the proportional function y=-5x, which one is correct ( ) A. When x=1, y=5 B． Its image is a straight line passing through the origin C. y increases as x increases D. Its image passes through the first and third quadrants

【Answer】B; Solution: A. When x=1, y=-5, wrong; B. The graph of the proportional function is a straight line passing through the origin, which is correct; C. According to k<0, the image passes through the second and fourth quadrants, and y decreases as x increases, which is wrong; D. The image passes through the second and fourth quadrants, which is an error; Therefore choose B.

Then which of the following relationships is correct ( )

【Answer】B;

3. Application of proportional function

A. A is faster than B B. B is faster than A C. A and B move at the same speed D. uncertain

【Answer】A;

A.2.5 meters B.2 meters C.1.5 meters D.1 meters

【Answer】C;

2. Practice to consolidate

1. Multiple choice questions

1. The straight line passes through the point (0, 0) and the point ( ) A. (-1, -3) B. (1, 3) C. (1, -3) D. (3, -1)

1. 【Answer】C;

2. Among the following functions, which one is a proportional function ( )

2. 【Answer】A;

3. In the following graphs, what represents the graph of the function y=-kx (k<0) is ( )

3. 【Answer】C; [Analysis] Solution: ∵k＜0, ∴﹣k＞0, ∴The value of function y=-kx (k<0) increases with the increase of independent variable x, and the function is a proportional function, Therefore choose: C.

4. 【Answer】C;

5. Regarding the function y=2x, which of the following conclusions is correct ( ) A. The graph of the function all passes through the point (2, 1) B． The function graphs all pass through the second and fourth quadrants C. y increases as x increases D. No matter what value x takes, there is always y>0

5. 【Answer】C; [Analysis] A. The function graph passes through the point (2, 4), which is an error; B. the function graph passes through the first and third quadrants, which is an error; C. y increases with the increase of x, which is correct; D. when x>0, y>0 can only exist, which is wrong; so choose C.

6. 【Answer】D;

2. Fill in the blanks

10. It is known that the proportional function y=(1﹣m)x|m-2|, and y decreases as x increases, then the value of m is .

10.【Answer】3; [Analysis] Solution: ∵This function is a proportional function, Solve to get m=3.

11. [Answer] 4, one, three

12. If the function y=(2m 6)x (1-m) is a proportional function, then the value of m is .

12.【Answer】1;

3. Answer questions

(2) It takes a few minutes for this candle to burn out.

13.【Analysis】

14. It is known that y is a proportional function of x, and the graph of the function passes through point A (-3, 6). (1) Find the functional relationship between y and x; (2) When x=-6, find the corresponding function value y;

14.【Analysis】 Solution: (1) Let the analytical formula of the proportional function be y=kx, ∵The image passes through point (-3, 6), ∴﹣3k=6， The solution is k=-2, Therefore, the relationship expression of this function is y=-2x; (2) Substituting x=-6 into the analytical formula, we can get: y=12;

15. If the image of the proportional function passes through point A (-5, 3),

15.【Analysis】