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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

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proportional function

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Outline

Trigonometric functions
- 499
- 1
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Lines and angles
- 100
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quadratic radical
- 101
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special parallelogram
- 42
Mason·Carter
The concept of trigonometric functions
- 20
MM
round
- 36
Mason·Carter
The concept and properties of functions
- 49
Mason·Carter
Parallel and intersection lines (1)
- 77
Mason·Carter
Equations (Systems) and their applications
- 38
EllaGrace
One-element equation
- 37
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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】