"Power Function" PPT courseware on the concept and properties of functions

Description

"Power Function" PPT courseware on the concept and properties of functions

Part One: Learning Objectives

Understand the concept of power function and be able to find the analytical formula of power function

Master the image characteristics of five power functions y=x, y=x2, y=x3, y=x12, y=x-1

With the help of the images of the five power functions, master the properties of the five power functions and be able to apply them

Power function PPT, part 2: independent learning

Problem guide

Preview textbooks P89-P91 and think about the following questions:

1. What is the definition of a power function?

2. What are the characteristics of the analytical expression of a power function?

3. What are the characteristics of the graph of a power function?

4. What are the properties of power functions?

A preliminary exploration of new knowledge

1. The concept of power function

Generally, the function y=_____ is called a power function, where _____ is the independent variable and _____ is a constant.

■Instructions from famous teachers

Characteristics of power functions

(1) The coefficient of xα is 1.

(2) The base of xα is the independent variable.

(3) The exponent of xα is constant.

Only when these three conditions are met at the same time is it a power function. For functions of the form y=(2x)α, y=2x5, y=xα+6, etc., they are not power functions.

2. The image and properties of power function

(1) Images of five common power functions

(2) Properties of five types of power functions

self-test

Judge whether it is true or false (mark “√” if it is correct and “×” if it is wrong)

(1) The graphs of power functions all pass through the points (0, 0) and (1, 1). ()

(2) The image of the power function must not appear in the fourth quadrant. ()

(3) When the power exponent α is 1, 3, or 12, the power function y=xα is an increasing function. ()

(4) When the power exponent α=-1, the power function y=xα is a decreasing function in the domain of definition. ()

Which of the following functions is a power function ()

A． y＝2x3　B． y=2x2-1

C. y=1x D． y=3x2

Among the following four figures, the image of y=x-12 is roughly ()

If y=mxα+(2n-4) is a power function, then m+n=________.

Power function PPT, the third part: interactive teaching and practice

The concept of power function

(1) The following functions: ①y=x3; ②y=12x; ③y=4x2; ④y=x5+1; ⑤y=(x-1)2; ⑥y=x; ⑦y=ax(a>1). The number of power functions is ()

A． 1B． 2

C. 3D． 4

(2) If the function y=(m2+2m-2)xm is a power function and an increasing function in the first quadrant, then the value of m is ()

A． 1B. -3

C. -1 D． 3

[Analysis] (1) In ②⑦, the independent variable

(2) Because the function y=(m2+2m-2)xm is a power function and an increasing function in the first quadrant, m2+2m-2=1, m>0, so m=1.

regular method

How to determine whether a function is a power function

The basis for judging whether a function is a power function is whether the function is in the form of y=xα (α is a constant), that is, the analytical expression of the function is in the form of a power and must satisfy:

(1) The exponent is a constant;

(2) The base is the independent variable;

(3)The coefficient is 1.

Images and applications of power functions

It is known that the graph of the power function f(x)=xα passes through points P2, 14. Try to draw the graph of f(x) and point out the domain and monotonic interval of the function.

[Solution] Because the image of f(x)=xα passes through points P2, 14,

So f(2)=14, that is, 2α=14,

We get α=-2, that is, f(x)=x-2. The image of f(x) is as shown in the figure. The definition domain is (-∞, 0) ∪ (0, +∞), and the monotonic decreasing interval is ( 0, +∞), and the monotonically increasing interval is (-∞, 0).

regular method

Principles to be grasped when solving power function graph problems

(1) Determine the size of the power exponent based on the height of the image. The relevant conclusions are: ① On (0, 1), the larger the exponent, the closer the power function image is to the x-axis (abbreviated to mean that the large image is low); ② In (0,1) 1, +∞), the larger the index, the further away the power function graph is from the x-axis (abbreviated as the height of the large graph).

(2) Determine the relationship between the power index α and 0 and 1 based on the image, that is, judge based on the image of the power function in the first quadrant (similar to y=x-1 or y=x12 or y=x3).

Power function PPT, part 4: feedback on achievement of standards

1. It is known that the function f(x)=(a2-a-1)x1a-2 is a power function, then the value of the real number a is ()

A． -1 or 2 B． -2 or 1

C. -1 D． 1

2. The image of the power function y=f(x) passes through the point (3, 3), then f(x)()

A． is an even function and is an increasing function on (0, +∞)

B． is an even function, and is a decreasing function on (0, +∞)

C. is an odd function and is a decreasing function on (0, +∞)

D. It is neither an odd function nor an even function, and it is an increasing function on (0, +∞)

3. The minimum value of function y=x-3 on the interval [-4,-2] is ________.

4. It is known that y=(m2+2m-2)xm2-1+2n-3 is a power function with a domain of R. Find the values ​​of m and n.

Keywords: Free download of PPT courseware for compulsory course No. 1 Mathematics of High School People's Education A version, power function PPT download, concept and properties of functions PPT download, .PPT format;

For more information about the "Concept and Properties of Functions Power Functions" PPT courseware, please click the "Concepts and Properties of Functions ppt Power Functions ppt" tag.

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Update Time: 2024-09-06

This template belongs to Mathematics courseware People's Education High School Mathematics Edition A Compulsory Course 1 industry PPT template

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